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Peter Benner - Publications

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Books

[B9]  Model Reduction and Approximation: Theory and Algorithms
Peter Benner, Albert Cohen, Mario Ohlberger, and Karen Willcox (Eds.)
Computational Science and Engineering Vol. 15, SIAM Publications, Philadelphia, PA, 2017.
[ISBN: 978-1-611974-81-2] DOI: 10.1137/1.9781611974829
[B8]  Model Reduction of Parametrized Systems
Peter Benner, Mario Ohlberger, Anthony Patera, Gianluigi Rozza, and Karsten Urban (Eds.)
MS&A – Modeling, Simulation and Applications, Vol. 17, Springer International Publishing, 2017.
[ISBN: 978-3-319-58785-1] DOI: 10.1007/978-3-319-58786-8
[B7]  System Reduction for Nanoscale IC Design
Peter Benner (Ed.)
Mathematics in Industry, Vol. 20, Springer-Verlag, 2017.
[ISBN: 978-3-319-07235-7 (hardcover), 978-3-319-07236-4 (eBook)]
DOI: 10.1007/978-3-319-07236-4
[B6]  Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory: Festschrift in Honor of Volker Mehrmann
Peter Benner, Matthias Bollhöfer, Daniel Kressner, Christian Mehl, and Tatjana Stykel (Eds.)
Springer International Publishing, 2015.
[ISBN: 978-3-319-15259-2 (hardcover), ISBN: 978-3-319-15260-8 (eBook)]
DOI: 10.1007/978-3-319-15260-8
[B5]  Modelo para las aspersiones con glifosato: frontera Ecuador-Colombia [in Spanish]
Peter Benner, Hermann Mena, and René Schneider
Shaker-Verlag, Aachen, 2014.
[ISBN: 978-3-8440-3061-7]
DOI: 10.2370/9783844030617
[B4]  Large-Scale Networks in Engineering and Life Sciences
Peter Benner, Rolf Findeisen, Dietrich Flockerzi, Udo Reichl, and Kai Sundmacher (Eds.)
Modeling and Simulation in Science, Engineering and Technology, Birkhäuser, Boston, MA, 2014.
[ISBN: 978-3-319-08436-7 (hardcover), 978-3-319-08437-4 (eBook)]
DOI: 10.1007/978-3-319-08437-4
[B3]  Trends in PDE Constrained Optimization
Günter Leugering, Peter Benner, Sebastian Engell, Andreas Griewank, Helmut Harbrecht, Michael Hinze, Rolf Rannacher, and Stefan Ulbrich (Eds.)
International Series of Numerical Mathematics, Vol. 165, Birkhäuser, Basel, 2014.
[ISBN: 978--3-319-05082-9 (hardcover), 978-3-319-05083-6 (eBook)]
DOI: 10.1007/978-3-319-05083-6
[B2]  Model Reduction for Circuit Simulation
Peter Benner, Michael Hinze, and E. Jan W. ter Maten (Eds.)
Lecture Notes in Electrical Engineering, Vol. 74, Springer-Verlag, 2011.
[ISBN: 978-94-007-0088-8 (hardcover), 978-94-007-0090-1 (paperback)]
Read online here.
DOI: 10.1007/978-94-007-0089-5
[B1]  Dimension Reduction of Large-Scale Systems
Peter Benner, Volker Mehrmann, and Danny C. Sorensen (Eds.)
Lecture Notes in Computational Science and Engineering, Vol. 45, Springer-Verlag, Berlin/Heidelberg, June 2005.
[ISBN: 3-540-24545-6]
DOI: 10.1007/3-540-27909-1

Editorials

[E12]   [new] Preface: Model Reduction and Approximation: Theory and Algorithms
Peter Benner, Albert Cohen, Mario Ohlberger, and Karen Willcox
In P. Benner, A. Cohen, M. Ohlberger, and K. Willcox (Eds.) Model Reduction and Approximation: Theory and Algorithms, SIAM Publications, Philadelphia, PA, 2017.
DOI: 10.1137/1.9781611974829
[E11]  [new] Preface: System Reduction for Nanoscale IC Design
Peter Benner
In P. Benner (Ed.), System Reduction for Nanoscale IC Design, Mathematics in Industry, Vol. 20, pp. v-vii, Springer International Publishing, Cham. 2017.
DOI: 10.1007/978-3-319-07236-4
[E10] Model Order Reduction of Parameterized Systems (MoRePaS): Preface to the Special Issue of Advances in Computational Mathematics
Peter Benner, Mario Ohlberger, Anthony T. Patera, Gianluigi Rozza, Danny C. Sorensen, and Karsten Urban
Advances in Computational Mathematics, Vol. 41, Issue 5, pp. 955-960, 2015.
DOI: 10.1007/s10444-015-9443-y
[E9] Introduction to the special issue for EUCCO 2013
Peter Benner, Roland Herzog, Michael Hinze, Arnd Rösch, Anton Schiela, and Volker Schulz
Computational Optimization and Applications, Vol. 62, No. 1, pp. 1-3, 2015.
DOI: 10.1007/s10589-015-9776-y
[E8] Preface: Festschrift in Honor of Volker Mehrmann
Peter Benner, Matthias Bollhöfer, Daniel Kressner, Christian Mehl, and Tatjana Stykel
In P. Benner, M. Bollhöfer, D. Kressner, Ch. Mehl, and T. Stykel (Eds.), Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory: Festschrift in Honor of Volker Mehrmann, pp. v-xvii, Springer International Publishing, 2015. [ISBN: 978-3-319-15259-2]
DOI: 10.1007/978-3-319-15260-8
[E7] Introduction
Günter Leugering, Andreas Griewank, Stefan Ulbrich, Helmut Harbrecht, Peter Benner, Rolf Rannacher, Michael Hinze, and Sebastian Engell
In G. Leugering, P. Benner, S. Engell, A. Griewank, H. Harbrecht, M. Hinze, R. Rannacher, and S. Ulbrich (Eds.), Trends in PDE Constrained Optimization, International Series of Numerical Mathematics, Vol. 165, pp. 1-4, Springer International Publishing, Switzerland, 2014. [ISBN: 978-3-319-05082-9]
DOI: 10.1007/978-3-319-05083-6_1
[E6] Introduction to Part III Adaptivity and Model Reduction
Peter Benner and Rolf Rannacher
In G. Leugering, P. Benner, S. Engell, A. Griewank, H. Harbrecht, M. Hinze, R. Rannacher, and S. Ulbrich (Eds.), Trends in PDE Constrained Optimization, International Series of Numerical Mathematics, Vol. 165, pp. 249-250, Springer International Publishing, Switzerland, 2014. [ISBN: 978-3-319-05082-9]
DOI: 10.1007/978-3-319-05083-6_16
[E5] Structured Matrix Computations in Non-Euclidean Geometries: Algorithms and Applications
Peter Benner, Miloud Sadkane, and Ahmed Salam
BIT Numerical Mathematics, Vol. 54, No. 1, pp. 1-5, 2014.
DOI: 10.1007/s10543-014-0479-z.
[E4] Preface of the Guest-Editors
Peter Benner and Daniel Kressner
GAMM Mitteilungen, Vol. 36, No. 1, pp. 6-7, 2013.
DOI: 10.1002/gamm.201310001.
[E3] A Mathematical Biography of Danny C. Sorensen
Peter Benner, Mark Embree, Richard B. Lehoucq, and C.T. Kelley
Linear Algebra and its Applications, Vol. 436, Issue 8, pp. 2717-2724, 2012.
DOI: 10.1016/j.laa.2012.01.031.
[E2] Editorial: Large-Scale Matrix Equations of Special Type
Peter Benner
Numerical Linear Algebra with Applications, Vol. 15, No. 9, pp. 747-754, 2008.
DOI: 10.1002/nla.621.
[E1] Preface Special Issue on "Order reduction of large-scale systems"
Peter Benner, Roland W. Freund, Danny C. Sorensen, and Andras Varga
Linear Algebra and its Applications, Vol. 415, Issues 2-3, pp. 231-234, 2006.
DOI: 10.1016/j.laa.2006.01.018.

Submitted articles

[S27]  [new] An Inexact Newton-Krylov Method for Stochastic Eigenvalue Problems
Peter Benner, Akwum Onwunta, and Martin Stoll
arXiv Preprint arXiv:1710.09470, October 2017.
[S26]  [new] Comparison of Model Order Reduction Methods for Optimal Sensor Placement for Thermo-Elastic Models
Peter Benner, Roland Herzog, Norman Lang, Ilka Riedel, and Jens Saak
Submitted, October 2017.
[S25]  [new] Model Reduction of Descriptor Systems with the MORLAB Toolbox
Peter Benner and Steffen W. R. Werner
Submitted, September 2017.
[S24]  [new] Faster and more Accurate Computation of the H-Norm via Optimization
Peter Benner and Tim Mitchell
arXiv Preprint arXiv:1707.02497, July 2017.
[S23]  [new] Model Reduction of Controlled Fokker-Planck and Liouville-von Neumann Equations
Peter Benner, Tobias Breiten, Carsten Hartmann, and Burkhard Schmidt
arXiv Preprint arXiv:1706.09882 , July 2017.
[S22] A Local Discontinuous Galerkin Method for Dirichlet Boundary Control Problems
Peter Benner and Hamdullah Yücel
Submitted, May 2017.
[S21] Fast Solution of the Poisson-Boltzmann Equation with nonaffine Parametrized Boundary Conditions Using the Reduced Basis Method
Peter Benner Lihong Feng, Cleophas Kweyu, and Matthias Stein
arXiv Preprint arXiv:1705.08349, May 2017.
[S20] Optimal Control Problems Constraint by the Stochastic Navier-Stokes Equations with Multiplicative Lévy Noise
Peter Benner and Christoph Trautwein
Submitted, May 2017.
[S19] A Direct Index 1 DAE Model of Gas Networks
Peter Benner, Maike Braukmüller, and Sara Grundel
Submitted, April 2017.
[S18] An Iterative Model Reduction Scheme for Quadratic-Bilinear Descriptor Systems with an Application to Navier-Stokes Equations
Peter Benner and Pawan Goyal
arXiv Preprint arXiv:1705.00934, April 2017.
[S17] Balanced Truncation Model Order Reduction For Quadratic-Bilinear Control Systems
Peter Benner and Pawan Goyal
arXiv Preprint arXiv:1705.00160, April 2017.
[S16] Interpolatory Model Reduction for Quadratic-Bilinear Systems using Error Estimators
Mian Ilyas Ahmad, Peter Benner, and Lihong Feng
Submitted, April 2017.
[S15] GPU Accelerated, Storage-Efficient Implementation of the QR Decomposition
Peter Benner, Martin Köhler, and Carolin Penke
Submitted, March 2017.
[S14] Low-Rank Computation of Posterior Covariance Matrices in Bayesian Inverse Problems
Peter Benner, Yue Qiu, and Martin Stoll
arXiv Preprint arXiv:1703.05638, March 2017.
[S13] Solving Optimal Control Problems Governed by Random Navier-Stokes Equations Using Low-Rank Methods
Peter Benner, Sergey Dolgov, Akwum Onwunta, and Martin Stoll
arXiv Preprint arXiv:1703.06097, March 2017.
[S12] Hankel-Norm Approximation of Descriptor Systems
Steffen Werner and Peter Benner
Submitted, December 2016.
[S11] Space-time Galerkin POD with Application in Optimal Control of Semi-linear Parabolic Partial Differential Equations
Peter Benner and Jan Heiland
arXiv Preprint arXiv:1611.04050, November 2016.
[S10] H2-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems
Peter Benner, Pawan Goyal, and Serkan Gugercin
arXiv Preprint arXiv:1610.03279v1, October 2016.
[S9] Model Reduction of Linear Multi-Agent Systems by Clustering and Associated H2- and H-Error Bounds
Hidde-Jan Jongsma, Petar Mlinarić, Sara Grundel, Peter Benner, and Harry L. Trentelman
arXiv Preprint arXiv:1610.02432v1, September 2016.
[S8] Model Reduction by Iterative Error System Approximation
Lihong Feng, Athanasios C. Antoulas, and Peter Benner
Submitted August 2016.
[S7] Relative Perturbation Theory for Quadratic Eigenvalue Problems
Peter Benner, Xin Liang, Suzana Miodragović, and Ninoslav Truhar
arXiv Preprint arXiv:1602.03420v2 [math.NA], February 2016.
[S6] Balanced Truncation of Linear Time-Invariant Systems over Finite-frequency Ranges
Xin Du and Peter Benner
arXiv Preprint arXiv:1602.04402v1 [cs.SY], February 2016.
[S5] Finite-Frequency Model Order Reduction of Linear Systems via Parameterized Frequency-dependent Balanced Truncation
Xin Du and Peter Benner
arXiv Preprint arXiv:1602.04408v1 [cs.SY], February 2016.
[S4] A Note on a Family of Generalized Procrustes Problems
Jens Fankhänel and Peter Benner
Submitted September 2015
[S3] Some Remarks on the Complex J-Symmetric Eigenproblem
Peter Benner, Heike Faßbender, and Chao Yang
MPI Magdeburg Preprint MPIMD/15-12, July 2015.
[S2] Adaptive Discontinuous Galerkin Approximation of Optimal Control Problems Governed by Transient Convection-Diffusion Equations
Hamdullah Yücel, Martin Stoll, and Peter Benner
MPI Magdeburg Preprint MPIMD/15-11, July 2015.
[S1] Balanced Truncation for Descriptor Systems with Many Terminals
Peter Benner and André Schneider
MPI Magdeburg Preprint MPIMD/13-17, October 2013.

Refereed articles in journals

NOTE: The versions of the papers that can be downloaded from this page are often the official journal versions with restricted access. Often, preliminary versions in the form of preprints are available. In any case, we advise you to prefer the published articles as they contain the most recent versions. Electronic reprints of the official versions are available on request.

[J180]  [new] Range-Separated Tensor Format for Many-Particle Modeling
Peter Benner, Venera Khoromskaia, and Boris N. Khoromskij
SIAM Journal on Scientific Computing, accepted 18 October 2017.
Preliminary version appeared as arXiv Preprint arXiv:1606.09218, June 2016.
[J179]  [new] L-Norm Computation for Large-Scale Descriptor Systems Using Structured Iterative Eigensolvers
Peter Benner, Ryan Lowe, and Matthias Voigt
Numerical Algebra, Control and Optimization (NACO), accepted 12 October 2017.
[J178]  [new] Large-Scale Computation of L-Norms by a Greedy Subspace Method
Nicat Aliyev, Peter Benner, Emre Mengi, Paul Schwerdtner, and Matthias Voigt
SIAM Journal on Matrix Analysis and Applications, accepted 30 August 2017. Preliminary version appeared as arXiv Preprint arXiv:1705.10086, May 2017.
[J177]  [new] A Linear Quadratic Control Problem for the Stochastic Heat Equation Driven by Q-Wiener Processes
Peter Benner and Christoph Trautwein
Journal of Mathematical Analysis and Applications, Vol. 457, No. 1, pp. 776-802, 2018.
DOI: 10.1016/j.jmaa.2017.08.052
[J176]  [new] Exponential Stability and Stabilization of Extended Linearizations via Continuous Updates of Riccati-Based Feedback
Peter Benner and Jan Heiland
International Journal of Robust and Nonlinear Control, available online 20 September 2017.
DOI: 10.1002/rnc.3949
Preliminary version appeared as arXiv Preprint arXiv:1607.08441, July 2016.
[J175]  [new] Singular Perturbation Approximation for Linear Systems with Lévy Noise
Peter Benner and Martin Redmann
Stochastics and Dynamics, accepted 22 July 2017.
DOI: 10.1142/S0219493718500338
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-22, December 2015.
[J174]  [new] RADI: A Low-Rank ADI-type Algorithm for Large Scale Algebraic Riccati Equations
Peter Benner, Zvonimir Bujanović, Patrick Kürschner, and Jens Saak
Numerische Mathematik, published online 24 July 2017.
DOI: 10.1007/s00211-017-0907-5
Preliminary version appeared as "A Low-Rank Quadratic ADI Algorithm for Algebraic Riccati Equations", arXiv Preprint arXiv:1510.00040 [math.NA], September 2015.
[J173]  [new] Optimal Control of a Stefan Problem Fully Coupled with Navier-Stokes-Equations and Mesh Movement
Björn Baran, Peter Benner, Jan Heiland, and Jens Saak
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, accepted 3 June 2017.
[J172]  [new] Computing the Stochastic H-Norm by a Newton Iteration
Tobias Damm, Peter Benner, and Jan Hauth
IEEE Control Systems Letters, Vol. 1, No. 1, pp. 92-97, 2017.
DOI: 10.1109/LCSYS.2017.2707409
Preliminary version appeared as arXiv Preprint arXiv:1703.04440, March 2017.
[J171]  [new] An H2-Type Error Bound for Balancing-Related Model Order Reduction of Linear Systems with Lévy Noise
Peter Benner and Martin Redmann
Systems & Control Letters, Vol. 105, pp. 1-5, 2017.
DOI: 10.1016/j.sysconle.2017.04.004
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-20, December 2015.
[J170]  [new] An Index-aware Parametric Model Order Reduction Method for Parametrized Quadratic Differential-Algebraic Equations
Nicodemus Banagaaya, Peter Benner, Lihong Feng, Peter Meuris, and Wim Schoenmaker
Applied Mathematics and Computation, Vol. 319, pp. 409-424, available online 1 November 2017.
DOI: 10.1016/j.amc.2017.04.024
[J169]  [new] Moment-Matching Based Model Reduction for Stokes-Type Quadratic-Bilinear Descriptor Systems
Mian Ilyas Ahmad, Peter Benner, Pawan Goyal, and Jan Heiland
Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), published online 11 April 2017.
DOI: 10.1002/zamm.201500262 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-18, October 2015.
[J168]  [new] Adaptive POD-DEIM Basis Construction and its Application to a Nonlinear Population Balance System
Lihong Feng, Michael Mangold, and Peter Benner
AIChE Journal, Vol 63, No. 9, pp. 3832–3844, 2017.
DOI: 10.1002/aic.15749
[J167]  [new] Some a Posteriori Error Bounds for Reduced Order Modelling of (Non-)Parametrized Linear Systems
Lihong Feng, Athanasios C. Antoulas, and Peter Benner
ESAIM: Mathematical Modelling and Numerical Analysis, accepted March 16, 2017.
DOI: 10.1051/m2an/2017014 Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-17, October 2015.
[J166]  [new] POD-DEIM for Efficient Reduction of a Dynamic 2D Catalytic Reactor Model
Peter Benner, Jens Bremer, Lihong Feng, Pawan Goyal, and Kai Sundmacher
Computers & Chemical Engineering, Vol. 106, pp. 777-783, 2017.
DOI: 10.1016/j.compchemeng.2017.02.032
[J165] Adaptive Symmetric Interior Penalty Galerkin Method for Boundary Control Problems
Peter Benner and Hamdullah Yücel
SIAM Journal on Numerical Analysis, Vol. 55, No. 2, pp. 1101–1133, 2017.
DOI: 10.1137/15M1034507
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-13, August 2015.
[J164] Structure Preserving Iterative Methods for Periodic Projected Lyapunov Equations and their Application in Model Reduction of Periodic Descriptor Systems Peter Benner and Mohammad-Sahadet Hossain
Numerical Algorithms, Vol. 74, No. 225, published online 23 February 2017.
DOI: 10.1007/s11075-017-0288-y
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-08, July 2015.
[J163] Fast Iterative Solution of the Bethe-Salpeter Eigenvalue Problem Using Low-Rank and QTT Tensor Approximation
Peter Benner, Sergey Dolgov, Venera Khoromskaia, and Boris N. Khoromskij
Journal of Computational Physics, Vol. 334, pp. 221–239, 2017.
DOI: 10.1016/j.jcp.2016.12.047.
Preliminary version appeared as arXiv Preprint arXiv:1602.02646v1 [math.NA], February 2016.
[J162] An Isoperimetric Optimal Control Problem for a Non-Isothermal Chemical Reactor with Periodic Inputs
Alexander Zuyev, Andreas Seidel-Morgernstern, and Peter Benner
Chemical Engineering Science, Vol. 161, pp. 206–214, 2017.
DOI: 10.1016/j.ces.2016.12.025.
[J161] Extending the Gauss-Huard Method for the Solution of Lyapunov Matrix Equations and Matrix Inversion
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
Concurrency and Computation: Practice and Experience, Vol. 29, No. 9, pp. e4076 (13pp.), 2017.
DOI: 10.1002/cpe.4076.
[J160] Krylov Subspace-based Model Reduction for a Class of Bilinear Descriptor Systems
Pawan Goyal, Mian Ilyas Ahmad, and Peter Benner
Journal of Computational and Applied Mathematics, Vol. 315, pp. 303–318, 2017.
DOI: 10.1016/j.cam.2016.11.009.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-07, May 2015.
[J159] Implicit Volterra Series Interpolation for Model Reduction of Bilinear Systems
Mian Ilyas Ahmad, Ulrike Baur, and Peter Benner
Journal of Computational and Applied Mathematics, Vol. 316, pp. 15-28, 2017.
DOI: 10.1016/j.cam.2016.09.048.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-21, December 2015.
[J158] Accelerating Optimization and Uncertainty Quantification of Nonlinear SMB Chromatography Using Reduced-Order Models
Yongjin Zhang, Lihong Feng, Andreas Seidel-Morgenstern, and Peter Benner
Computers & Chemical Engineering, Vol. 96, pp. 237-247, 2017.
DOI: 10.1016/j.compchemeng.2016.09.017.
[J157] Parametric Modeling and Model Order Reduction for (Electro-)Thermal Analysis of Nanoelectronic Structures
Lihong Feng, Yao Yue, Nicodemus Banagaaya, Peter Meuris, Wim Schoenmaker, and Peter Benner
Journal of Mathematics in Industry, Vol. 6, Art. 10 (16pp.), 2016.
DOI: 10.1186/s13362-016-0030-8.
[J156] Multipoint Interpolation of Volterra Series and H2-Model Reduction for a Family of Bilinear Descriptor Systems
Peter Benner and Pawan Goyal
Systems & Control Letters, Vol. 97, pp. 1-11, 2016.
DOI: 10.1016/j.sysconle.2016.08.008.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-16, September 2015.
[J155] Structure Preserving Model Order Reduction of Large Sparse Second-Order Index-1 Systems and Application to a Mechatronics Model
Peter Benner, Jens Saak, and M. Monir Uddin
Mathematical and Computer Modelling of Dynamical Systems, Vol. 22, Issue 6, pp. 509-523, 2016.
DOI: 10.1080/13873954.2016.1218347.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-23, December 2014.
[J154] Nanoelectronic COupled Problems Solutions - nanoCOPS: Modelling, Multirate, Model Order Reduction, Uncertainty Quantification, Fast Fault Simulation
E. J. W. ter Maten, P. A. Putek, M. Günther, R. Pulch, C. Tischendorf, Ch. Strohm, W. Schoenmaker, P. Meuris, B. De Smedt, P. Benner, L. Feng, N. Banagaaya, Y. Yue et al.
Journal of Mathematics in Industry, Vol. 7, Art. 2 (19pp.), 2017.
DOI: 10.1186/s13362-016-0025-5.
Updated and extended version of OP17.
[J153] Krylov Subspace Methods for Model Reduction of Quadratic-Bilinear Systems
Mian Ilyas Ahmad, Peter Benner, and Imad M. Jaimoukha
IET Control Theory & Applications, Vol. 10, Issue 16, pp. 2010–2018, 2016.
DOI: 10.1049/iet-cta.2016.0415.
[J152] An Inexact Low-Rank Newton-ADI Method for Large-Scale Algebraic Riccati Equations
Peter Benner, Matthias Heinkenschloss, Jens Saak, and Heiko K. Weichelt
Applied Numerical Mathematics, Vol. 108, pp. 125-142, June 2016.
DOI: 10.1016/j.apnum.2016.05.006.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-06, May 2015.
[J151] Dual Pairs of Generalized Lyapunov Inequalities and Balanced Truncation of Stochastic Linear Systems
Peter Benner, Tobias Damm, and Yolanda Rocio Rodriguez Cruz
IEEE Transactions on Automatic Control, Vol. 62, No. 2, pp. 782-791, 2017.
DOI: 10.1109/TAC.2016.2572881.
[J150] Numerical Solution of the Infinite-Dimensional LQR Problem and the Associated Riccati Differential Equations
Peter Benner and Hermann Mena
Journal of Numerical Mathematics, published online 04 May 2016.
DOI: 10.1515/jnma-2016-1039.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-13, August 2012.
[J149] Computation of Thermo-Elastic Deformations on Machine Tools - A study of Numerical Methods
Andreas Naumann, Norman Lang, Marian Partzsch, Michael Beitelschmidt, Peter Benner, Axel Voigt, and Jörg Wensch
Production Engineering Research & Development, Vol. 10, Issue 3, pp. 253-263, 2016.
DOI: 10.1007/s11740-016-0674-7.
[J148] Trigonometric Spline and Spectral Bounds for the Solution of Linear Time-Periodic Systems
Peter Benner, Jonas Denißen, and Ludwig Kohaupt
Journal of Applied Mathematics and Computing, Vol. 54, Issue 1, pp. 127–157, 2017.
DOI: 10.1007/s12190-016-1001-3.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/16-01, January 2016.
[J147] Low-Rank Solvers for Unsteady Stokes-Brinkman Optimal Control Problem with Random Data
Peter Benner, Sergey Dolgov, Akwum Onwunta, and Martin Stoll
Computer Methods in Applied Mechanics and Engineering, Vol. 304, pp. 26-54, 2016.
DOI: 10.1016/j.cma.2016.02.004.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-10, July 2015.
[J146] Balancing Energy and Performance in Dense Linear System Solvers for Hybrid ARM+GPU
Juan Pablo Silva, Ernesto Dufrechou, Pablo Ezzatti, Enrique S. Quintana-Ortí, Alfredo Remón, and Peter Benner
CLEI Electronic Journal, Vol. 19, Issue 1, Paper 2, 2016.
DOI: 10.19153.19.1.2.
[J145] Block-diagonal Preconditioning for Optimal Control Problems Constrained by PDEs with Uncertain Inputs
Peter Benner, Akwum Onwunta, and Martin Stoll
SIAM Journal on Matrix Analysis and Applications, Vol. 37, No. 2, pp. 491–518, 2016.
DOI: 10.1137/15M1018502.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-05, April 2015.
[J144] A Reduced Basis Approach for Calculation of the Bethe-Salpeter Excitation Energies using Low-Rank Tensor Factorizations
Peter Benner, Venera Khoromskaia, and Boris N. Khoromskij
Molecular Physics, Vol. 114, Issue 7-8, pp. 1148-1161, 2016.
DOI: 10.1080/00268976.2016.1149241.
[J143] Frequency-Limited Balanced Truncation with Low-Rank Approximations
Peter Benner, Patrick Kürschner, and Jens Saak
SIAM Journal on Scientific Computing, Vol. 38, Issue 1, pp. A471–A499, 2016.
DOI: 10.1137/15M1030911.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-09, July 2015.
[J142] Time-dependent Dirichlet Conditions in Finite Element Discretizations
Peter Benner and Jan Heiland
ScienceOpen Research, available online 3 October 2015.
DOI: 10.14293/S2199-1006.1.SOR-MATH.AV2JW3.v1.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-03, September 2012.
[J141] On the Solution of Large-Scale Algebraic Riccati Equations by Using Low-Dimensional Invariant Subspaces
Peter Benner and Zvonimir Bujanović
Linear Algebra and Its Applications, Vol. 488, pp. 430-459, 2016.
DOI: 10.1016/j.laa.2015.09.027.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-15, August 2014.
[J140] A Fully Adaptive Scheme for Model Order Reduction Based on Moment-Matching
Lihong Feng, Jan G. Korvink, and Peter Benner
IEEE Transactions on Components, Packaging, and Manufacturing Technology, Vol. 5, No. 12, pp. 1872-1884, 2015.
DOI: 10.1109/TCPMT.2015.2491341.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-14, September 2012.
[J139] An Efficient Output Error Estimation for Model Order Reduction of Parametrized Evolution Equations
Yongjin Zhang, Lihong Feng, and Peter Benner
SIAM Journal on Scientific Computing, Vol. 37, No. 6, pp. B910–B936, 2015.
DOI: 10.1137/140998603.
[J138] Unleashing GPU Acceleration for Symmetric Band Linear Algebra Kernels and Model Reduction
Peter Benner, Ernestro Dufrechou, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
Cluster Computing, Vol. 18, Issue 4, pp. 1351-1362, 2015.
DOI: 10.1007/s10586-015-0489-x.
[J137] A Discontinous Galerkin Method for Optimal Control Problems Governed by a System of Convection-Diffusion PDEs with Nonlinear Reaction Terms
Hamdullah Yücel, Martin Stoll, and Peter Benner
Computers and Mathematics with Applications, Vol. 70, Issue 10, pp. 2414-2431, 2015.
DOI: 10.1016/j.camwa.2015.09.006.
MPI Magdeburg Preprint MPIMD/13-10, July 2013.
[J136] Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell's Equations
Martin W. Hess, Sara Grundel, and Peter Benner
IEEE Transactions on Microwave Theory and Techniques, Vol. 63, Issue 11, pp. 3549-3557, 2015.
DOI: 10.1109/TMTT.2015.2473157.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-19, November 2014.
[J135] Algorithm 961 - FORTRAN 77 Subroutines for the Solution of Skew-Hamiltonian/Hamiltonian Eigenproblems
Peter Benner, Vasile Sima, and Matthias Voigt
ACM Transactions on Mathematical Software (TOMS), Vol. 42, Issue 3, no. 24, 2016.
DOI: 10.1145/2818313.
[J134] Balancing Based Model Reduction for Structured Index-2 Unstable Descriptor Systems with Application to Flow Control
Peter Benner, Jens Saak, and M. Monir Uddin
Numerical Algebra, Control and Optimization (NACO), Vol. 6, Issue 1, pp. 1-20, 2016.
DOI: 10.3934/naco.2016.6.1.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-20, November 2014.
[J133] Modeling Glyphosate Aerial Spray Drift at the Ecuador-Colombia Border
Peter Benner, Hermann Mena, and René Schneider
Applied Mathematical Modelling, Vol. 40, No. 1, 373–387. 2016.
DOI: 10.1016/j.apm.2015.04.057.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-08, April 2014.
[J132] Recycling BiCGSTAB with an Application to Parametric Model Order Reduction
Kapil Ahuja, Eric de Sturler, Lihong Feng, and Peter Benner
SIAM Journal on Scientific Computing, Vol. 37, Issue 5, pp. S429-S446, 2015.
DOI: 10.1137/140972433.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-21, November 2013.
[J131] Model Reduction for Stochastic Systems
Peter Benner and Martin Redmann
Stochastic Partial Differential Equations: Analysis and Computations, Vol. 3, Issue 3, pp. 291-338, 2015.
DOI: 10.1007/s40072-015-0050-1.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-03, February 2014.
[J130] Accelerating PDE Constrained Optimization by the Reduced Basis Method: Application to Batch Chromatography
Yongjin Zhang, Lihong Feng, Suzhou Li, and Peter Benner
International Journal for Numerical Methods in Engineering, Vol. 104, Issue 11, pp. 983-1007, 2015.
DOI: 10.1002/nme.4950.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-09, May 2014.
[J129] A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
Peter Benner, Serkan Gugercin, and Karen Willcox
SIAM Review, Vol. 57, Issue 4, pp. 483–531, 2015.
DOI: 10.1137/130932715.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-14, August 2013.
[J128] Low-Rank Newton-ADI Methods for Large Nonsymmetric Algebraic Riccati Equations
Peter Benner, Patrick Kürschner, and Jens Saak
Journal of the Franklin Institute, Vol. 353, Issue 5, pp. 1147-1167, 2016.
DOI: 10.1016/j.jfranklin.2015.04.016.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-21, November 2014.
[J127] Semi-Active Damping Optimization of Vibrational Systems using the Parametric Dominant Pole Algorithm
Peter Benner, Patrick Kürschner, Zoran Tomljanović, and Ninoslav Truhar
Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), Vol. 96, Issue 5, pp. 604-619, 2016.
DOI: 10.1002/zamm201400158.
MPI Magdeburg Preprint MPIMD/14-12, July 2014.
[J126] Towards the Identification of Heat Induction in Chip Removing Processes via an Optimal Control Approach
Norman Lang, Jens Saak, Peter Benner, Steffen Ihlenfeldt, Steffen Nestmann, and Klaus Schädlich
Production Engineering: Development & Research, Vol. 9, Issue 3, pp. 343-349, 2015.
DOI: 10.1007/s11740-015-0608-9.
[J125] Low Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients
Peter Benner, Akwum Onwunta, and Martin Stoll
SIAM/ASA Journal on Uncertainty Quantification, Vol. 3, No. 1, pp. 622–649, 2015.
DOI: 10.1137/130937251.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-13, August 2013.
[J124] Model Order Reduction for Coupled Problems: Survey
Peter Benner and Lihong Feng
Applied and Computational Mathematics: An International Journal, Vol. 14, No. 1, pp. 3-22, 2015.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-02, February 2015.
[J123] Riccati-Based Boundary Feedback Stabilization of Incompressible Navier-Stokes Flow
Eberhard Bänsch, Peter Benner, Jens Saak, and Heiko K. Weichelt
SIAM Journal on Scientific Computing, Vol. 37, No. 2, pp. A832–A858, 2015.
DOI: 10.1137/140980016.
[J122] Parametric Model Order Reduction with a Small H2-Error Using Radial Basis Functions
Peter Benner, Sara Grundel, Nils Hornung
Advances in Computational Mathematics, Vol. 41, Issue 5, pp. 1231-1253, 2015.
DOI: 10.1007/s10444-015-9410-7.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-01, January 2014.
[J121] Nonlinear Model Reduction of a Continuous Fluidized Bed Crystallizer
Michael Mangold, Dmytro Khlopov, Stefan Palis, Lihong Feng, Peter Benner, Daniel Binev, and Andreas Seidel-Morgenstern
Journal of Computational and Applied Mathematics, Vol. 289, pp. 253-266, 2015.
DOI: 10.1016/j.cam.2015.01.028.
[J120] Two-Sided Projection Methods for Nonlinear Model Order Reduction
Peter Benner and Tobias Breiten
SIAM Journal on Scientific Computing, Vol. 37, Issue 2, pp. B239–B260, 2015.
DOI: 10.1137/14097255X.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-12, June 2012.
[J119] Positive Operators and Stable Truncation
Peter Benner, Tobias Damm, Martin Redmann, and Yolanda Rocio Rodriguez Cruz
Linear Algebra and its Applications, Vol. 498, pp. 74-87, 2016.
DOI: 10.1016/j.laa.2014.12.005.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-11, July 2014.
[J118] Fast and Reliable Noise Estimation for Hyperspectral Subspace Identification
Peter Benner, Vedran Novaković, Antonio Plaza, Enrique S. Quintana-Ortí, and Alfredo Remón
IEEE Geoscience and Remote Sensing Letters, Vol. 12, Issue 6, pp. 1199-1203, June 2015.
DOI: 10.1109/LGRS.2014.2388133.
[J117] Uncertainty Quantification for Maxwell's Equations Using Stochastic Collocation and Model Order Reduction
Peter Benner and Judith Schneider
International Journal for Uncertainty Quantification, Vol. 5, No. 3, pp. 195–208, 2015.
DOI: 10.1615/Int.J.UncertaintyQuantification.2015010170.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-19, October 2013.
[J116] Computing the Eigenvalues of Symmetric H2-Matrices by Slicing the Spectrum
Peter Benner, Steffen Börm, Thomas Mach, and Knut Reimer
Computing and Visualization in Science, Vol. 16, No. 6, pp. 271-282, published online 4 March 2015.
DOI: 10.1007/s00791-015-0238-y.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-06, March 2014.
[J115] Extending Lyapack for the Solution of Band Lyapunov Equations on Hybrid CPU-GPU Platforms
Peter Benner, Ernesto Dufrechou, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
The Journal of Supercomputing, Vol. 71, No. 2, pp. 740-750, 2015.
DOI: 10.1007/s11227-014-1322-7.
[J114] Self-Generating and Efficient Shift Parameters in ADI Methods for Large Lyapunov and Sylvester Equations
Peter Benner, Patrick Kürschner, and Jens Saak
Electronic Transactions on Numerical Analysis, Vol. 43, pp. 142-162, 2014.
DOI: 10.17617/2.2071065.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-18, October 2013.
[J113] Parallel Model Order Reduction of Sparse Electromagnetic/Circuit Models
Giovanni De Luca, Giulio Antonini, and Peter Benner
ACES Journal, Vol. 30, No. 1, S1-21, January 2015.
[J112] Adaptive Discontinuous Galerkin Methods for State Constrained Optimal Control Problems Governed by Convection Diffusion Equations
Hamdullah Yücel and Peter Benner
Computational Optimization and Applications, Vol. 62, pp. 291-321, 2015.
DOI: 10.1007/s10589-014-9691-7.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-16, September 2013.
[J111] Model Order Reduction for a Family of Linear Systems with Application in Parametric and Uncertain Systems
Peter Benner and Sara Grundel
Applied Mathematics Letters, Vol. 39, pp. 1-6, 2015.
DOI: 10.1016/j.aml.2014.08.002.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-05, March 2014.
[J110] Rational Interpolation Methods for Symmetric Sylvester Equations
Peter Benner and Tobias Breiten
Electronic Transactions on Numerical Analysis, Vol. 42, pp. 147-164, 2014.
DOI: 10.17617/2.2060858.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-23, December 2013.
[J109] Model Reduction for Linear Simulated Moving Bed Chromatography Systems Using Krylov-Subspace Methods
Suzhou Li, Yao Yue, Lihong Feng, Andreas Seidel-Morgenstern, and Peter Benner
AIChE Journal, Vol. 60, No. 11, pp. 3773–3783, 2014.
DOI: 10.1002/aic.14561.
[J108] Model Order Reduction for Linear and Nonlinear Systems: a System-Theoretic Perspective
Peter Benner, Ulrike Baur, and Lihong Feng
Archives of Computational Methods in Engineering, Vol. 21, No. 4, pp. 331–358, 2014.
DOI: 10.1007/s11831-014-9111-2.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-07, March 2014.
[J107] Model Order Reduction for Systems with Moving Loads
Norman Lang, Jens Saak, and Peter Benner
at-Automatisierungstechnik, Vol. 62, No. 7, pp. 512-522, 2014.
DOI: 10.1515/auto-2014-1095.
[J106] Parametric Model Order Reduction of Thermal Models Using the Bilinear Interpolatory Rational Krylov Algorithm
Peter Benner and Angelika Bruns
Mathematical and Computer Modelling of Dynamical Systems, Vol. 21, Issue 2, pp. 103-129, 2015.
DOI: 10.1080/13873954.2014.924534.
The hyperlink to the paper (title link) allows 50 free downloads of the full text. Afterwards, it directs to the paper abstract.
[J105] A Reduced Basis Method for Microwave Semiconductor Devices with Geometric Variations
Martin W. Hess and Peter Benner
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 33, No. 4, pp. 1071-1081, 2014.
DOI: 10.1108/COMPEL-12-2012-0377.
[J104] A Structured Pseudospectral Method for H-Norm Computation of Large-Scale Descriptor Systems
Peter Benner and Matthias Voigt
Mathematics of Control, Signals, and Systems, Vol. 26, No. 2, pp. 303-338, 2014.
DOI: 10.1007/s00498-013-0121-7.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-10, May 2012.
[J103] Using Surrogate Models for Efficient Optimization of Simulated Moving Bed Chromatography
Suzhou Li, Lihong Feng, Peter Benner, and Andreas Seidel-Morgenstern
Computers & Chemical Engineering, Vol. 67, pp. 121-132, 2014.
DOI: 10.1016/j.compchemeng.2014.03.024.
[J102] Numerical Solution of Projected Algebraic Riccati Equations
Peter Benner and Tatjana Stykel
SIAM Journal on Numerical Analysis, Vol. 52, No. 2, pp. 581-600, 2014.
DOI: 10.1137/130923993
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-06, May 2013.
[J101] Trading Off Performance for Energy in Linear Algebra Operations with Applications in Control Theory
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
CLEI Electronic Journal, Vol. 17, No. 1, Paper 3 (12 pages), 2014.
DOI: 10.17617/2.2060863.
[J100] Computing Real Low-Rank Solutions of Sylvester Equations by the Factored ADI Method
Peter Benner and Patrick Kürschner
Computers and Mathematics with Applications, Vol. 67, Issue 9, pp. 1656–1672, 2014.
DOI: 10.1016/j.camwa.2014.03.004
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-05, May 2013.
[J99] On Optimality of Approximate Low-Rank Solutions of Large-Scale Matrix Equations
Peter Benner and Tobias Breiten
Systems & Control Letters Vol. 67, pp. 55-64, 2014.
DOI: 10.1016/j.sysconle.2014.02.005
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-10, December 2011.
[J98] Low-Rank Iterative Methods of Periodic Projected Lyapunov Equations and their Application in Model Reduction of Periodic Descriptor Systems
Peter Benner, Mohammad-Sahadet Hossain, and Tatjana Stykel
Numerical Algorithms, Vol. 67, No. 3, pp. 669–690, 2014.
DOI: 10.1007/s11075-013-9816-6
Preliminary version appeared as Chemnitz Scientific Computing Preprints 11-01, TU Chemnitz, February 2011.
[J97] Solving Matrix Equations on Multi-Core and Many-Core Architectures
Peter Benner, Pablo Ezzatti, Hermann Mena, Enrique S. Quintana-Ortí, and Alfredo Remón
Algorithms, Vol. 6, No. 4, pp. 857-870, 2013.
DOI: 10.3390/a6040857
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-07, October 2011.
[J96] On the Squared Smith Method for Large-Scale Stein Equations
Peter Benner, Grece El Khoury, and Miloud Sadkane
Numerical Linear Algebra with Applications, Vol. 21, Issue 5, pp. 645-665, 2014.
DOI: 10.1002/nla.1918
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-15, September 2012.
[J95] Fast solution of Cahn-Hilliard Variational Inequalities using Implicit Time Discretization and Finite Elements
Jessica Bosch, Martin Stoll, and Peter Benner
Journal of Computational Physics, Vol. 262, pp. 38-57, 2014.
DOI: 10.1016/j.jcp.2013.12.053
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-01, January 2013.
[J94] A Factored Variant of the Newton Iteration for the Solution of Algebraic Riccati Equations via the Matrix Sign Function
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
Numerical Algorithms, Vol. 66, No. 2, pp. 363-377, 2014.
DOI: 10.1007/s11075-013-9739-2
[J93] Numerical Solution of Large and Sparse Continuous Time Algebraic Matrix Riccati and Lyapunov Equations: A State of the Art Survey
Peter Benner and Jens Saak
GAMM Mitteilungen, Vol. 36, No. 1, pp. 32-52, 2013.
DOI: 10.1002/gamm.201310003
[J92] Discontinuous Galerkin Finite Element Methods with Shock-Capturing for Nonlinear Convection Dominated Models
Hamdullah Yücel, Martin Stoll, and Peter Benner
Computers & Chemical Engineering, Vol. 58, pp. 278-287, 2013.
DOI: 10.1016/j.compchemeng.2013.07.011
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-03, January 2013.
[J91] Rosenbrock Methods for Solving Differential Riccati Equations
Peter Benner and Hermann Mena
IEEE Transactions on Automatic Control, Vol. 58, No. 11, pp. 2950-2956, 2013.
DOI: 10.1109/TAC.2013.2258495
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-06, October 2011.
© IEEE.
[J90] A Non-Conforming Composite Quadrilateral Finite Element Pair for Feedback Stabilization of the Stokes Equations
Peter Benner, Jens Saak, Friedhelm Schieweck, Piotr Skrzypacz, and Heiko K. Weichelt
Journal of Numerical Mathematics, Vol. 22, No. 3, pp. 191-220, 2014.
DOI: 10.1515/jnma-2014-0009
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-19, October 2012.
[J89] Fast Evaluation of Time-Harmonic Maxwell's Equations Using the Reduced Basis Method
Peter Benner and Martin W. Hess
IEEE Transactions on Microwave Theory and Techniques, Vol. 61, No. 6, pp. 2265-2274, 2013.
DOI: 10.1109/TMTT.2013.2258167
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-17, October 2012.
[J88] An Improved Numerical Method for Balanced Truncation for Symmetric Second-Order Systems
Peter Benner, Patrick Kürschner, and Jens Saak
Mathematical and Computer Modelling of Dynamical Systems, Vol. 19, No. 6, pp. 593-615, 2013.
DOI: 10.1080/13873954.2013.794363.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-20, November 2012.
[J87] Efficient Solution of Large-Scale Saddle Point Systems Arising in Riccati-Based Boundary Feedback Stabilization of Incompressible Stokes Flow
Peter Benner, Jens Saak, Martin Stoll and Heiko K. Weichelt
SIAM Journal on Scientific Computing, Vol. 35, No. 5, pp. S150-S170, 2013.
DOI: 10.1137/120881312.
Preliminary version appeared as Preprint SPP1253-130 of the DFG Priority Programme 1253 Optimization with Partial Differential Equations, June 2012.
[J86] The LR Cholesky Algorithm for Symmetric Hierarchical Matrices
Peter Benner and Thomas Mach
Linear Algebra and its Applications, Vol. 439, No. 4, pp. 1150-1166, 2013.
DOI: 10.1016/j.laa.2013.03.001.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-05, February 2012.
[J85] Spectral Characterization and Enforcement of Negative Imaginariness for Descriptor Systems
Peter Benner and Matthias Voigt
Linear Algebra and its Applications, Vol. 439, No. 4, pp. 1104-1129, 2013.
DOI: 10.1016/j.laa.2012.12.044.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-09, April 2012.
[J84] Low Rank Methods for a Class of Generalized Lyapunov Equations and Related Issues
Peter Benner and Tobias Breiten
Numerische Mathematik, Vol. 124, No. 3, pp. 441-470, 2013.
DOI: 10.1007/s00211-013-0521-0.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-03, February 2012.
[J83] Subspace Recycling Accelerates the Parametric Macro‐modeling of MEMS
Lihong Feng, Peter Benner, and Jan G. Korvink
International Journal for Numerical Methods in Engineering, Vol. 94, No. 1, pp. 84-110, 2013.
DOI: 10.1002/nme.4449.
Preliminary version appeared as Fast Model Reduction of Parametric Systems using Subspace Recycling MPI Magdeburg Preprint MPIMD/12-08, March 2012.
[J82] Model Reduction of an Elastic Crankshaft for Elastic Multibody Simulations
Christine Nowakowski, Patrick Kürschner, Peter Eberhard, and Peter Benner
Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), Vol. 93, No. 4, pp. 198-216, 2013.
DOI: 10.1002/zamm.201200054.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-07, March 2012.
[J81] Computation of a Compact State Space Model for an Adaptive Spindle Head Configuration with Piezo Actuators using Balanced Truncation
M. Monir Uddin, Jens Saak, Burkhard Kranz, and Peter Benner
Production Engineering, Vol. 6, No. 6, pp. 577-586, 2012.
DOI: 10.1007/s11740-012-0410-x.
[J80] Matrix Inversion on CPU-GPU Platforms with Applications in Control Theory
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
Concurrency and Computation: Practice and Experience, Vol. 25, No. 8, pp. 1170-1182, 2013.
DOI: 10.1002/cpe.2933.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-02, February 2012.
[J79] Interpolation-Based H2-Model Reduction of Bilinear Control Systems
Peter Benner and Tobias Breiten
SIAM Journal on Matrix Analysis and Applications, Vol. 33, No. 3, pp. 859-885, 2012.
DOI: 10.1137/110836742.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-02, June 2011.
[J78] HPC en simulación y control a gran escala [in Spanish]
Peter Benner, Pablo Ezzatti, Hermann Mena, Enrique S. Quintana-Ortí, and Alfredo Remón
Revista ELEMENTOS, Vol. 3, No. 3, pp. 9-35, 2013.
[J77] Efficient Handling of Complex Shift Parameters in the Low-Rank Cholesky Factor ADI method
Peter Benner, Patrick Kürschner, and Jens Saak
Numerical Algorithms, Vol. 62, No. 2, pp. 225-251, 2013.
DOI: 10.1007/s11075-012-9569-7.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-08, October 2011.
[J76] A Mathematical Biography of Danny C. Sorensen
Peter Benner, Mark Embree, Richard B. Lehoucq, and C.T. Kelley
Linear Algebra and its Applications, Vol. 436, Issue 8, pp. 2717-2724, 2012.
DOI: 10.1016/j.laa.2012.01.031.
[J75] The Preconditioned Inverse Iteration for Hierarchical Matrices
Peter Benner and Thomas Mach
Numerical Linear Algebra with Applications, Vol. 20, No. 1, pp. 150-166, 2013.
DOI: 10.1002/nla.1830.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-01, February 2011.
[J74] Optimal Damping of Selected Eigenfrequencies Using Dimension Reduction
Peter Benner, Zoran Tomljanović, and Ninoslav Truhar
Numerical Linear Algebra with Applications, Vol. 20, No. 1, pp. 1-17, 2013.
DOI: 10.1002/nla.833.
Preliminary version appeared as Preprint 1/2011, Department of Mathematics, J. J. Strossmayer University of Osijek, March 2011.
[J73] Computing All or Some Eigenvalues of Symmetric ℋ-Matrices
Peter Benner and Thomas Mach
SIAM Journal on Scientific Computing, Vol. 34, Issue 1, pp. A485-A496, 2012.
DOI: 10.1137/100815323.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/10-01, November 2010.
[J72] L-Norm Computation for Continuous-Time Descriptor Systems Using Structured Matrix Pencils
Peter Benner, Vasile Sima, and Matthias Voigt
IEEE Transactions on Automatic Control, Vol. 57, No. 1, pp. 233-238, 2012.
DOI: 10.1109/TAC.2011.2161833.
[J71] Interpolatory Projection Methods for Parameterized Model Reduction
Ulrike Baur, Christopher Beattie, Peter Benner, and Serkan Gugercin
SIAM Journal on Scientific Computing, Vol. 33, Issue 5, pp. 2489-2518, 2011.
DOI: 10.1137/090776925.
Preliminary version appeared as Chemnitz Scientific Computing Preprints 09-08, TU Chemnitz, November 2009.
[J70] Generalized Tangential Interpolation for Model Reduction of Discrete-Time MIMO Bilinear Systems
Peter Benner, Tobias Breiten, and Tobias Damm
International Journal of Control, Vol. 84, No. 8 pp. 1398-1407, 2011.
DOI: 10.1080/00207179.2011.601761.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/10-02, December 2010.
[J69] Robust Formulas for Optimal H Controllers
Peter Benner, Ralph Byers, Philip Losse, Volker Mehrmann, and Hongguo Xu
Automatica, Vol. 47, No. 12, pp. 2639-2646, 2011.
DOI: 10.1016/j.automatica.2011.09.013.
Preliminary version appeared as Preprint 20-2010, Preprint series of the Institute of Mathematics, Technische Universität Berlin, September 2010.
[J68] Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems
Peter Benner and Tobias Damm
SIAM Journal on Control and Optimization, Vol. 49, No. 2, pp. 686-711, 2011.
DOI: 10.1137/09075041X.
[J67] A Mixed-Precision Algorithm for the Solution of Lyapunov Equations on Hybrid CPU-GPU Platforms
Peter Benner, Pablo Ezzatti, Daniel Kressner, Enrique S. Quintana-Ortí, and Alfredo Remón
Parallel Computing, Vol. 37, Issue 8, pp. 439–450, 2011.
DOI: 10.1016/j.parco.2010.12.002.
Preliminary version appeared as Research Report No. 2009-40, Seminar für Angewandte Mathematik, ETH Zürich, December 2009.
[J66] Efficient Balancing-Based MOR for Large-Scale Second-Order Systems
Peter Benner and Jens Saak
Mathematical and Computer Modelling of Dynamical Systems, Vol. 17, No. 2, pp. 123-143, 2011.
Author Posting. (c) Taylor & Francis, 2011.
This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in January 2011.
DOI: 10.1080/13873954.2010.540822.
[J65] Dimension Reduction for Damping Optimization in Linear Vibrating Systems
Peter Benner, Zoran Tomljanović, and Ninoslav Truhar
Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), Vol. 91, No. 3, pp. 179–191, 2011.
Editor's choice of this ZAMM issue!
DOI: 10.1002/zamm.201000077.
Preliminary version appeared as Preprint 2/2010, Department of Mathematics, J. J. Strossmayer University of Osijek, April 2010.
[J64] On the Numerical Solution of Large-Scale Sparse Discrete-Time Riccati Equations
Peter Benner and Heike Faßbender
Advances in Computational Mathematics, Vol. 35, No. 2-4, pp. 119-147, 2011.
DOI: 10.1007/s10444-011-9174-7.
Preliminary version appeared as Chemnitz Scientific Computing Preprints 09-11, TU Chemnitz, December 2009.
[J63] Parameter Preserving Model Order Reduction for MEMS Applications
Ulrike Baur, Peter Benner, Andreas Greiner, Jan G. Korvink, Jan Lienemann, and Christian Moosmann
Mathematical and Computer Modelling of Dynamical Systems, Vol. 17, No. 4, pp. 297-317, 2011.
DOI: 10.1080/13873954.2011.547658.
[J62] A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process
Peter Benner, Heike Faßbender, and Martin Stoll
Linear Algebra and its Applications, Vol. 435, Issue 3, pp. 578-600, 2011.
DOI: 10.1016/j.laa.2010.04.048.
Preliminary version appeared as OCCAM Report Number 09/32, Oxford Centre for Collaborative Applied Mathematics, July 2009.
[J61] On the QR Decomposition of H-Matrices.
Peter Benner and Thomas Mach
Computing, Vol. 88, No. 3-4, pp. 111-129, 2010.
DOI: 10.1007/s00607-010-0087-y.
See also Chemnitz Scientific Computing Preprints09-04, TU Chemnitz, July 2009.
[J60] Die SLICOT-Toolboxen für Matlab (The SLICOT-Toolboxes for Matlab) [German]
Peter Benner, Daniel Kressner, Vasile Sima, and Andras Varga
at-Automatisierungstechnik, Vol. 58, Issue 1, pp. 15-25, 2010.
DOI: 10.1524/auto.2010.0814.
For an English version, see The SLICOT Toolboxes - a Survey, SLICOT Working Note 2009-1, August 2009.
[J59] Modale versus moderne Ordnungsreduktionsverfahren: Effiziente Simulation von Werkzeugmaschinen [German]
Thomas Bonin, Michael Zäh, Andreas Soppa, Heike Faßbender, Jens Saak, and Peter Benner
MECHATRONIK, Vol. 11-12/2009, pp. 46-47, 2009.
[J58] On the ADI Method for Sylvester Equations
Peter Benner, Reng-Cang Li, and Ninoslav Truhar
Journal of Computational and Applied Mathematics, Vol. 233, No. 4, pp. 1035-1045, 2009.
DOI: 10.1016/j.cam.2009.08.108.
[J57] Model Reduction for Parametric Systems Using Balanced Truncation and Interpolation [German]
Ulrike Baur and Peter Benner
at-Automatisierungstechnik Vol. 57, No. 8, pp. 411-419, 2009.
DOI: 10.1524/auto.2009.0787.
[J56] A Rational SHIRA Method for the Hamiltonian Eigenvalue Problem
Peter Benner and Cedric Effenberger
Taiwanese Journal of Mathematics, Vol. 14, No. 3A, pp. 805-823, 2010.
See also Chemnitz Scientific Computing Preprints 08-08, TU Chemnitz, December 2008.
[J55] Solving Large-Scale Quadratic Eigenvalue Problems with Hamiltonian Eigenstructure using a Structure-Preserving Krylov Subspace Method
Peter Benner, Heike Faßbender, and Martin Stoll
Electronic Transactions on Numerical Analysis, Vol. 29, pp. 212-229, 2008.
See also Numerical Analysis Group Research Report NA-07/03, Oxford University, February 2007.
[J54] Cross-Gramian Based Model Reduction for Data-Sparse Systems
Ulrike Baur and Peter Benner
Electronic Transactions on Numerical Analysis, Vol. 31, pp. 256-270, 2008.
[J53] Numerical Solution of Large Lyapunov Equations, Riccati Equations, and Linear-Quadratic Control Problems
Peter Benner, Jing-Rebecca Li, and Thilo Penzl
Numerical Linear Algebra with Applications, Vol. 15, No. 9, pp. 755-777, 2008.
DOI: 10.1002/nla.622
[J52] Gramian-Based Model Reduction for Data-Sparse Systems
Ulrike Baur and Peter Benner
SIAM Journal on Scientific Computing, Vol. 31, No. 1, pp. 776-798, 2008.
DOI: 10.1137/070711578
See also Chemnitz Scientific Computing Preprints 07-01, TU Chemnitz, February 2007.
[J51] Solving Linear-Quadratic Optimal Control Problems on Parallel Computers
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Optimization Methods and Software, Vol. 23, No. 6, pp. 879-909, 2008.
DOI: 10.1080/10556780802058721
See also: Preprint SFB393/05-19, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, March 2006.
[J50] On the Parameter Selection Problem in the Newton-ADI Iteration for Large-Scale Riccati Equations
Peter Benner, Hermann Mena, and Jens Saak
Electronic Transactions on Numerical Analysis, Vol. 29, pp. 136-149, 2008.
[J49] Efficient Algorithms for Generalized Algebraic Bernoulli Equations based on the Matrix Sign Function
Sergio Barrachina, Peter Benner, and Enrique S. Quintana-Ortí
Numerical Algorithms, Vol. 46, No. 4, pp. 351-368, 2007.
DOI: 10.1007/s11075-007-9143-x
Partially extracted from [TR15].
[J48] A Robust Numerical Method for the $\gamma$-Iteration in $H_\infty$ Control
Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu
Linear Algebra and its Applications, Vol. 425, No. 2-3, pp. 548-570, 2007.
DOI: 10.1016/j.laa.2007.03.026
Revised version of [TR13].
[J47] On the Solution of the Rational Matrix Equation X = Q + LX^{-1}L^T
Peter Benner and Heike Faßbender
EURASIP Journal on Advances in Signal Processing, special issue on "Numerical Linear Algebra in Signal Processing Application", Vol. 2007, Article ID 21850, 10 pages, 2007.
DOI: 10.1155/2007/21850
See also: Chemnitz Scientific Computing Preprints 06-02, TU Chemnitz, September 2006.
[J46] Factorized Solution of Lyapunov Equations Based on Hierarchical Matrix Arithmetic
Ulrike Baur and Peter Benner
Computing, Vol. 78, No. 3, pp. 211-234, 2006.
DOI: 10.1007/s00607-006-0178-y
[J45] Stabilizing Large-Scale Generalized Systems on Parallel Computers Using Multithreading and Message-Passing
Peter Benner, Maribel Castillo, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Concurrency and Computation: Practice and Experience, Vol. 19, No. 4, pp. 531-542, 2007.
DOI: 10.1002/cpe.1148
[J44]  Partial Realization of Descriptor Systems
Peter Benner and Viatcheslav I. Sokolov
Systems & Control Letters, Vol. 55, Issue 11, pp. 929-938, 2006.
DOI: 10.1016/j.sysconle.2006.06.009
[J43] Evaluation of the Linear Matrix Equation Solvers in SLICOT
Martin Slowik, Peter Benner, and Vasile Sima
Journal of Numerical Analysis, Industrial and Applied Mathematics, Vol. 2, No. 1-2, pp. 11-34, 2007.
Extendend version appeared as SLICOT Working Note 2004-1, August 2004.
[J42] An Arithmetic for Matrix Pencils: Theory and New Algorithms
Peter Benner and Ralph Byers
Numerische Mathematik, Vol. 103, No. 4, pp. 539-573, 2006.
DOI: 10.1007/s00211-006-0001-x
[J41]  Numerische Methoden zur passivitätserhaltenden Modellreduktion (Numerical Methods for Passivity Preserving Model Reduction) (in German)
Peter Benner and Heike Faßbender
at-Automatisierungstechnik, Vol. 54, No. 4, pp. 153-160, 2006.
DOI: 10.1524/auto.2006.54.4.153
[J40]  Numerical Linear Algebra for Model Reduction in Control and Simulation
Peter Benner
GAMM Mitteilungen, Vol. 29, No. 2, pp. 275-296, 2006.
DOI: 10.1002/gamm.201490034
See also Preprint 18/2005, Fakultät für Mathematik, TU Chemnitz.
[J39] Parallel Solution of Large-Scale Algebraic Bernoulli Equations with the Matrix Sign Function Method
Sergio Barrachina, Peter Benner, and Enrique S. Quintana-Ortí
International Journal of Computational Science and Engineering, Vol. 4, No. 2, pp. 88-93, 2009.
DOI: 10.1504/IJCSE.2009.027000
Extended version of [CA45].
[J38] Algorithm 854: Fortran 77 Subroutines for Computing the Eigenvalues of Hamiltonian Matrices
Peter Benner and Daniel Kressner
ACM Transactions on Mathematical Software, Vol. 32, No. 2, pp. 352-373, 2006.
DOI: 10.1145/1141885.1141895
For the corresponding software visit the HAPACK homepage.
[J37] Solving Stable Sylvester Equations via Rational Iterative Schemes
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Journal of Scientific Computing, Vol. 28, No. 1, pp. 51-83, 2006.
DOI: 10.1007/s10915-005-9007-2
Note: in Algorithm 3, Step 9 must read: U := U-CB; in Example 1, the entries of the solution matrix X need to be negated.
[J36] Balancing Sparse Hamiltonian Eigenproblems
Peter Benner and Daniel Kressner
Linear Algebra and its Applications, Vol. 415, Issue 1, pp. 3-19, 2006.
Original available from ScienceDirect,
DOI: 10.1016/j.laa.2004.09.023
[J35] Partial Stabilization of Large-Scale Discrete-Time Linear Control Systems
Peter Benner, Maribel Castillo, and Enrique S. Quintana-Ortí
International Journal of Computational Science and Engineering, Vol. 1, No. 1, pp. 15-21, 2005.
DOI: 10.1504/IJCSE.2005.008907
See also [CA19]
[J34] Solving Large-Scale Control Problems
Peter Benner
IEEE Control Systems Magazine, Vol. 24, No. 1, pp. 44-59, 2004.
DOI: 10.1109/MCS.2004.1272745
[J33] Parallel Algorithms for Model Reduction of Discrete-Time Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
International Journal of System Sciences, Vol. 34, No. 5, pp. 319-333, 2003.
DOI: 10.1080/0020772031000158564
The retrievable version appeared as Berichte aus der Technomathematik, Report 00-18, December 2000.
[J32] State-Space Truncation Methods for Parallel Model Reduction of Large-Scale Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Parallel Computing, Vol. 29 (special issue on "Parallel and Distributed Scientific and Engineering Computing"), Issue 11-12, pp. 1701-1722, 2003.
DOI: 10.1016/j.parco.2003.05.013
[J31] Structure Preservation: A Challenge in Computational Control
Peter Benner, Daniel Kressner, and Volker Mehrmann
Future Generation Computer Systems, Vol. 19, Issue 7, pp. 1243-1252, 2003.
DOI: 10.1016/S0167-739X(03)00049-9
[J30] The Kleinman Iteration for Nonstabilizable Systems
Peter Benner, Vicente Hernández, and Antonio Pastor
Mathematics of Control, Signals, and Systems , Vol. 16, Issue 1,pp. 76-93, 2003.
DOI: 10.1007/s00498-003-0130-z
The retrievable version appeared as Berichte aus der Technomathematik, Report 99-11, October 1999.
[J29] Numerical Solution of Discrete Stable Linear Matrix Equations on Multicomputers
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Parallel Algorithms and Applications (since 2005: International Journal of Parallel, Emergent and Distributed Systems) Vol. 17, No. 2, pp. 127-146, 2002.
DOI: 10.1080/10637190208941436
Free preprint available at Berichte aus der Technomathematik, Report 99-13, November 1999.
[J28] Numerical Computation of Deflating Subspaces of Skew-Hamiltonian/Hamiltonian Pencils
Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu
SIAM Journal on Matrix Analysis and Applications, Vol. 24, No. 1, pp. 165-190, 2002.
DOI: 10.1137/S0895479800367439
For an extended version, including detailed algorithms, see [TR10]
.
[J27] Parallel Algorithms for LQ Optimal Control of Discrete-Time Periodic Linear Systems
Peter Benner, Ralph Byers, Rafael Mayo, Enrique S. Quintana-Ortí, and Vicente Hernández
Journal of Parallel and Distributed Computing, Vol. 62, Issue 2, pp. 306-325, 2002.
DOI: 10.1006/jpdc.2001.1790
The retrievable version appeared as Berichte aus der Technomathematik, Report 01-02, February 2001.
[J26] Efficient Numerical Algorithms for Balanced Stochastic Truncation
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
International Journal of Applied Mathematics and Computer Science, Vol. 11, No. 5, pp. 1123-1150, 2001.
The retrievable version appeared as Berichte aus der Technomathematik, Report 01-03, March 2001.
[J25] Perturbation Analysis for the Eigenvalue Problem of a Formal Product of Matrices
Peter Benner, Volker Mehrmann, and Hongguo Xu
BIT, Vol. 42, No. 1, pp. 1-43, 2002.
DOI: 10.1023/A:1021966001542
The retrievable version appeared as Berichte aus der Technomathematik, Report 00-01, January 2000.
[J24] A Hybrid Method for the Numerical Solution of Discrete-Time Algebraic Riccati Equations
Peter Benner and Heike Faßbender
Contemporary Mathematics, Vol. 280, pp. 255-269, 2001.
The retrievable version appeared as Berichte aus der Technomathematik, Report 99-12, October 1999.
[J23] Cholesky-like Factorizations of Skew-Symmetric Matrices
Peter Benner, Ralph Byers, Heike Faßbender, Volker Mehrmann, and David S. Watkins
Electronic Transactions on Numerical Analysis, Vol. 11, pp. 85-93, 2000.
[J22] Symplectic Balancing of Hamiltonian Matrices
Peter Benner
SIAM Journal on Scientific Computing, Vol. 22, No. 5, pp. 1885-1904, 2001.
DOI: 10.1137/S1064827500367993
[J21] Evaluating Products of Matrix Pencils and Collapsing Matrix Products
Peter Benner and Ralph Byers
Numerical Linear Algebra with Applications, Vol. 8, No. 6-7, pp. 357-380, 2001.
DOI: 10.1002/nla.251
[J20] Balanced Truncation Model Reduction of Large-Scale Dense Systems on Parallel Computers
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Mathematical and Computer Modelling of Dynamical Systems, Vol. 6, No.4, pp. 383-405, 2000.
DOI: 10.1076/mcmd.6.4.383.3658
The retrievable version appeared as Berichte aus der Technomathematik, Report 99-07, September 1999.
[J19] An Implicitly Restarted Symplectic Lanczos Method for the Symplectic Eigenvalue Problem
Peter Benner and Heike Faßbender
SIAM Journal on Matrix Analysis and Applications, Vol. 22, No. 3, pp. 682-713, 2001.
DOI: 10.1137/S0895479898343115
Retrieve preprint: Berichte aus der Technomathematik, Report 98-01, July 1998.
[J18] Algorithm 800: Fortran 77 Subroutines for Computing the Eigenvalues of Hamiltonian Matrices I: The Square-Reduced Method
Peter Benner, Ralph Byers, and Eric Barth
ACM Transactions on Mathematical Software, Vol. 26, No. 1, pp. 49-77, 2000.
DOI: 10.1145/347837.347852
For the corresponding software, click here (shell script, compressed using gzip).
See also: [TR5] and Peter Benner's software.
[J17] Solving Algebraic Riccati Equations on Parallel Computers Using Newton's Method with Exact Line Search
Peter Benner, Ralph Byers, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Parallel Computing, Vol. 26, No. 10, pp. 1345-1368, 2000.
DOI: 10.1016/S0167-8191(00)00012-0
The retrievable version appeared as Berichte aus der Technomathematik, Report 98-05, August 1998.
[J16] A Note on the Numerical Solution of Complex Hamiltonian and Skew-Hamiltonian Eigenvalue Problems
Peter Benner, Volker Mehrmann, and Hongguo Xu
Electronic Transactions on Numerical Analysis, Vol. 8, pp. 115-126, 1999.
[J15] Solving Stable Generalized Lyapunov Equations with the Matrix Sign Function
Peter Benner and Enrique S. Quintana-Ortí
Numerical Algorithms, Vol. 20, No. 1, pp. 75-100, 1999.
DOI: 10.1023/A:1019191431273
Preliminary version appeared as Preprint SFB393/97-23, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, October 1997.
[J14] Parallel Partial Stabilizing Algorithms for Large Linear Control Systems
Peter Benner, Maribel Castillo, Enrique S. Quintana-Ortí, and Vicente Hernández
The Journal of Supercomputing, Vol. 15, Issue 2, pp. 193-206, 2000.
DOI: 10.1023/A:1008108004247
The retrievable version appeared as Berichte aus der Technomathematik, Report 98-03, July 1998.
[J13] Parallel Distributed Solvers for Large Stable Generalized Lyapunov Equations
Peter Benner, José M. Claver, and Enrique S. Quintana-Ortí
DOI: 10.1142/S0129626499000165
Parallel Processing Letters, Vol. 9, No. 1, pp. 147-158, 1999.
[J12] SR and SZ Algorithms for the Symplectic (Butterfly) Eigenproblem
Peter Benner, Heike Faßbender, and David S. Watkins
Linear Algebra and its Applications, Vol. 287, Issue 1-3, pp. 41-76, 1999.
DOI: 10.1016/S0024-3795(98)10090-3
[J11] SLICOT - A Subroutine Library in Systems and Control Theory
Peter Benner, Volker Mehrmann, Vasile Sima, Sabine Van Huffel, and Andras Varga
Applied and Computational Control, Signals, and Circuits, Vol. 1, pp. 505-546, 1999.
The retrievable version appeared as NICONET Report 97-03, Working Group on Software, June 1997.
[J10] Computational Methods for Linear-Quadratic Optimization
Peter Benner
Rendiconti del Circolo Matematico di Palermo, Supplemento, Serie II, No. 58, pp. 21-56, 1999.
Extendend version appeared as Berichte aus der Technomathematik, Report 98-04, August 1998.
[J9] The Symplectic Eigenvalue Problem, the Butterfly Form, the SR Algorithm, and the Lanczos Method
Peter Benner and Heike Faßbender
Linear Algebra and its Applications, Vol. 275/276, pp. 19-47, 1998.
DOI: 10.1016/S0024-3795(97)10049-0
[J8] A Numerically Stable, Structure Preserving Method for Computing the Eigenvalues of Real Hamiltonian or Symplectic Pencils
Peter Benner, Volker Mehrmann, and Hongguo Xu
Numerische Mathematik, Vol. 78, No. 3, pp. 329-358, 1998.
DOI: 10.1007/s002110050315
[J7] An Exact Line Search Method for Solving Generalized Continuous-Time Algebraic Riccati Equations
Peter Benner and Ralph Byers
IEEE Transactions on Automatic Control, Vol. 43, No. 1, pp. 101-107, 1998.
See also: [TR3]
.
[J6] Two Connections between the SR and HR Eigenvalue Algorithms
Peter Benner, Heike Faßbender, and David S. Watkins
Linear Algebra and its Applications, Vol. 272, Issue 1-3, pp. 17-32, 1998.
DOI: 10.1016/S0024-3795(97)00279-6
[J5] A New Method for Computing the Stable Invariant Subspace of a Real Hamiltonian Matrix
Peter Benner, Volker Mehrmann and Hongguo Xu
Journal of Computational and Applied Mathematics, Vol. 86, Issue 1, pp. 17-43, 1997.
DOI: 10.1016/S0377-0427(97)00146-5
[J4] NICONET, a Network for Numerically Reliable Software in CACSD
Ad J.W. van den Boom, Sabine Van Huffel, and Peter Benner
Journal A - Benelux Quarterly Journal on Automatic Control, Vol. 38, No. 3, pp. 20-21, 1997.
[J3] Benchmarks for the Numerical Solution of Algebraic Riccati Equations
Peter Benner, Alan J. Laub, and Volker Mehrmann
IEEE Control Systems Magazine, Vol. 17, No. 5, pp. 18-28, 1997.
DOI: 10.1109/37.621466
See also: [TR1], [TR2]
[J2] An Implicitly Restarted Symplectic Lanczos Method for the Hamiltonian Eigenvalue Problem
Peter Benner and Heike Faßbender
Linear Algebra and its Applications, Vol. 263, pp. 75-111, 1997.
DOI: 10.1016/S0024-3795(96)00524-1
See also: [TR4]
[J1] A Multishift Algorithm for the Numerical Solution of Algebraic Riccati Equations
Gregory Ammar, Peter Benner, and Volker Mehrmann
Electronic Transactions on Numerical Analysis, Vol. 1, pp. 33-48, 1993.

Book chapters

[BC31]  [new] Reduced Representation of Power Grid Models
Peter Benner and André Schneider
In P. Benner (Ed.), System Reduction for Nanoscale IC Design, Mathematics in Industry, Vol. 20, pp. 87-134, Springer International Publishing, Cham. 2017.
DOI: 10.1007/978-3-319-07236-4_3
[BC30]  [new] Comparison of Methods for Parametric Model Order Reduction of Unsteady Problems
Ulrike Baur, Peter Benner, Bernard Haasdonk, Christian Himpe, Immanuel Maier, and Mario Ohlberger
In P. Benner, A. Cohen, M. Ohlberger, K. Willcox (Eds.), Model Reduction and Approximation: Theory and Algorithms, Chapter 9, pp. 377-407, SIAM Publications, Philadelphia, PA, 2017.
DOI: 10.1137/1.9781611974829.ch9
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-01, February 2015.
[BC29]  [new] Model Order Reduction Based on System Balancing
Peter Benner and Tobias Breiten
In P. Benner, A. Cohen, M. Ohlberger, K. Willcox (Eds.), Model Reduction and Approximation: Theory and Algorithms, Chapter 6, pp. 261-295, SIAM Publications, Philadelphia, PA, 2017.
DOI: 10.1137/1.9781611974829
[BC28]  [new] Truncated Gramians for Bilinear Systems and their Advantages in Model Order Reduction
Peter Benner, Pawan Goyal, and Martin Redmann
In P. Benner, M. Ohlberger, T. Patera, G. Rozza, K. Urban (Eds.), Model Reduction of Parametrized Systems, MS&A - Modeling, Simulation and Applications, Springer International Publishing, Cham, Vol. 17, pp. 285-300, 2017.
DOI: 10.1007/978-3-319-58786-8_18
[BC27]  [new] Reduced Basis Approximations for Maxwell’s Equations in Dispersive Media
Peter Benner and Martin W. Hess
In P. Benner, M. Ohlberger, T. Patera, G. Rozza, K. Urban (Eds.), Model Reduction of Parametrized Systems, MS&A - Modeling, Simulation and Applications, Springer International Publishing, Cham, Vol. 17, pp. 107-119, 2017.
DOI: 10.1007/978-3-319-58786-8_7
[BC26] Model Order Reduction for Differential-Algebraic Equations: a Survey
Peter Benner and Tatjana Stykel
In A. Ilchmann, T. Reis (Eds.), Surveys in Differential-Algebraic Equations IV, Differential-Algebraic Equations Forum, Springer International Publishing,  [new]pp. 107-160, 2017.
DOI: 10.1007/978-3-319-46618-7_3
A preliminary version is available as MPI Magdeburg Preprint MPIMD/15-19, November 2015.
[BC25] Theory and Numerical Solution of Differential and Algebraic Riccati Equations
Peter Benner
In P. Benner, M. Bollhöfer, D. Kressner, Ch. Mehl, and T. Stykel (Eds.), Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory, Part I, pp. 67-105, Springer International Publishing, 2015.
DOI: 10.1007/978-3-319-15260-8_4
[BC24] Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations
Peter Benner, Philip Losse, Volker Mehrmann, and Matthias Voigt
In A. Ilchmann, T. Reis (Eds.), Surveys in Differential-Algebraic Equations III, pp. 117-175, Differential-Algebraic Equations Forum, Springer International Publishing, 2015.
DOI: 10.1007/978-3-319-22428-2_3
A preliminary version with slightly different focus is available as Preprint [TR26]

[BC23] Matrix Equations and Model Reduction
Peter Benner, Tobias Breiten, and Lihong Feng
In Z. Bai, W. Gao, and Y. Su (Eds.),
Matrix Functions and Matrix Equations, Series in Contemporary Applied Mathematics, Chapter 3, pp. 50-75, World Scientific, 2015.
DOI: 10.1142/9789814675772_0003
[BC22] Model Order Reduction for Thermo-Elastic Assembly Group Models
Peter Benner, Norman Lang, and Jens Saak
In K. Großmann (Eds.), Thermo-energetic Design of Machine Tools, Lecture Notes in Production Engineering, Chapter 8/pp.85-93, Springer International Publishing, 2015. [ISBN: 978-3-319-12624-1]
DOI: 10.1007/978-3-319-12625-8_8
[BC21] LQG-Balanced Truncation Low-Order Controller for Stabilization of Laminar Flows
Peter Benner and Jan Heiland
In R. King (Ed.), Active Flow and Combustion Control 2014, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol. 127, pp. 365-379, Springer International Publishing, 2015. [ISBN: 978-3-319-11966-3]
DOI: 10.1007/978-3-319-11967-0_22
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/14-04, March 2014.
[BC20] Model Order Reduction of Differential Algebraic Equations Arising from the Simulation of Gas Transport Networks
Sara Grundel, Lennart Jansen, Nils Hornung, Tanja Clees, Caren Tischendorf, and Peter Benner
In S. Schöps, A. Bartel, M. Günther, E. J. W. ter Maten, and P. C. Müller (Eds.), Progress in Differential-Algebraic Equations, Differential-Algebraic Equations Forum, pp. 183-205, Springer-Verlag, Berlin/Heidelberg, 2014. [ISBN: 978-3-662-44925-7]
DOI: 10.1007/978-3-662-44926-4_9
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/13-09, June 2013.
[BC19] Model Order Reduction: Techniques and Tools
Peter Benner and Heike Faßbender
In J. Baillieul and T. Samad (Eds.), Encyclopedia of Systems and Control, Springer-Verlag, pp. 722-729, 2015. [ISBN: 978-1-4471-5057-2]
DOI: 10.1007/978-1-4471-5058-9_142
[BC18] Model Reduction
Peter Benner
In N. J. Higham et al. (Eds.), Princeton Companion to Applied Mathematics, Princeton University Press, Princeton, NJ., Part II-26, pp. 117-119, 2015.
[BC17] Model Order Reduction for PDE Constrained Optimization
Peter Benner, Ekkehard Sachs, and Stefan Volkwein
In G. Leugering, P. Benner, S. Engell, A. Griewank, H. Harbrecht, M. Hinze, R. Rannacher, and S. Ulbrich (Eds.), Trends in PDE Constrained Optimization, International Series of Numerical Mathematics, Vol. 165, pp. 303-326, Birkhäuser, Basel, 2014. [ISBN: 978-3-319-05082-9]
DOI: 10.1007/978-3-319-05083-6_19
[BC16] Optimal Control-Based Feedback Stabilization of Multi-Field Flow Problems
Eberhard Bänsch, Peter Benner, Jens Saak, and Heiko K. Weichelt
In G. Leugering, P. Benner, S. Engell, A. Griewank, H. Harbrecht, M. Hinze, R. Rannacher, and S. Ulbrich (Eds.), Trends in PDE Constrained Optimization, International Series of Numerical Mathematics, Vol. 165, pp. 173-188, Birkhäuser, Basel, 2014. [ISBN: 978-3-319-05082-9]
DOI: 10.1007/978-3-319-05083-6_11
[BC15] A Robust Algorithm for Parametric Model Order Reduction Based on Implicit Moment Matching
Peter Benner and Lihong Feng
In A. Quarteroni and G. Rozza (Eds.), Reduced Order Methods for Modeling and Computational Reduction, MS&A - Modeling, Simulation and Applications, Vol. 9, pp. 159-185, Springer International Publishing, 2014. [ISBN: 978-1-4614-7550-7]
DOI: 10.1007/978-3-319-02090-7_6
[BC14] Control Theory
Peter Benner
In Leslie Hogben (Ed.), Handbook of Linear Algebra, Second Edition, Chapter 80, Chapman & Hall/CRC, 2014. [ISBN: 978-1-4665-0728-9]
Updated and revised version of BC8.
[BC13] Computing Surrogates for Gas Network Simulation using Model Order Reduction
Sara Grundel, Nils Hornung, Bernhard Klaassen, Peter Benner, and Tanja Clees
In S. Koziel and L. Leifsson (Eds.), Surrogate-Based Modeling and Optimization, pp. 189-212, Springer-Verlag, 2013. [ISBN: 978-1-4614-7550-7]
DOI: 10.1007/978-1-4614-7551-4_9
[BC12] Unleashing CPU-GPU Acceleration for Control Theory Applications
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
In I. Caragiannis et al. (Eds.), Euro-Par 2012, Parallel Processing Workshops., Lecture Notes in Computer Science, Vol. 7640, pp. 102-111, Springer-Verlag, Berlin/Heidelberg, 2013. [ISBN: 978-3-642-36948-3]
DOI: 10.1007/978-3-642-36949-0_13
[BC11] System-Level Modeling of MEMS by Means of Model Order Reduction (Mathematical Approximations) - Mathematical Background
Lihong Feng, Peter Benner, and Jan G. Korvink
In T. Bechthold, G. Schrag, and L. Feng (Eds.), System-Level Modeling of MEMS, Advanced Micro & Nanosystems, Vol. 10, pp. 53-93, Wiley-VCH Verlag, Weinheim, Germany, 2013. [ISBN-13: 978-3-5273-1903-9]
DOI: 10.1002/9783527647132.ch3
[BC10] Stabilization of Incompressible Flow Problems by Riccati-Based Feedback
Eberhard Bänsch and Peter Benner
In G. Leugering, S. Engell, A. Griewank, M. Hinze, R. Rannacher, V. Schulz, M. Ulbrich, and S. Ulbrich (Eds.), Constrained Optimization and Optimal Control for Partial Differential Equations, International Series of Numerical Mathematics, Vol. 160, pp. 5-20, Birkhäuser, Basel, 2012.
DOI: 10.1007/978-3-0348-0133-1
[BC9] Partial Stabilization of Descriptor Systems Using Spectral Projectors
Peter Benner
In P. Van Dooren, S. Bhattacharyya, R. Chan, V. Olshevsky, and A. Routray (Eds.), Numerical Linear Algebra in Signals, Systems and Control, Lecture Notes in Electrical Engineering, Vol. 80, pp. 55-76, Springer-Verlag, Dordrecht, 2011.
DOI: 10.1007/978-94-007-0602-6_3
[BC8]  Control Theory
Peter Benner
In Leslie Hogben (Ed.), Handbook of Linear Algeba, Chapter 57, Chapman & Hall/CRC, 2006.[ISBN-13: 978-1-58488-510-8]
[BC7]  Numerical Solution of Optimal Control Problems for Parabolic Systems
Peter Benner, Sabine Görner, and Jens Saak
In K.-H. Hoffmann and A. Meyer (Eds.), Parallel Algorithms and Cluster Computing: Implementations, Algorithms and Applications, Vol. 52 of Lecture Notes in Computational Science and Engineering, pp. 151-169, Springer-Verlag, Berlin, Heidelberg, New York, 2006. [ISBN/ISSN: 3-540-33539-0]
DOI: 10.1007/3-540-33541-2_9
[BC6] Model Reduction Based on Spectral Projection Methods
Peter Benner and Enrique S. Quintana-Ortí
In P. Benner, V. Mehrmann, and D.C. Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Ch. 1, Lecture Notes in Computational Science and Engineering, Vol. 45, pp. 5-48, Springer-Verlag, Berlin/Heidelberg, June 2005.
DOI: 10.1007/3-540-27909-1_1
[BC5] A Semi-Discretized Heat Transfer Model for Optimal Cooling of Steel Profiles
Peter Benner and Jens Saak
In P. Benner, V. Mehrmann, and D.C. Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Ch. 19, Lecture Notes in Computational Science and Engineering, Vol. 45, pp. 353-356, Springer-Verlag, Berlin/Heidelberg, June 2005.
DOI: 10.1007/3-540-27909-1_19
[BC4] Skew-Hamiltonian and Hamiltonian Eigenvalue Problems: Theory, Algorithms and Applications
Peter Benner, Daniel Kressner, and Volker Mehrmann
In Z. Drmač, M. Marušić, and Z. Tutek (Eds.), Proceedings of the Conference on Applied Mathematics and Scientific Computing, pp. 3-39. Springer-Verlag, 2005. [ISBN: 978-1-4020-3196-0]
DOI: 10.1007/1-4020-3197-1_1
[BC3] A Model Reduction Web Environment for Very Large Linear Dynamical Systems
Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In V.Y. Pan and L.T. Yang (Eds.), Parallel and Distributed Scientific and Engineering Computing: Practice and Experience, Advances in Computation: Theory and Practice, Vol. 15, pp. 23-33, NOVA Science Publishers, Hauppauge, NY, 2004. [ISBN:1-59033-956-8]
[BC2] A Portable Subroutine Library for Solving Linear Control Problems on Distributed Memory Computers
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In G. Cooperman, E. Jessen, and G.O. Michler (Eds.), Workshop on Wide Area Networks and High Performance Computing, Essen (Germany), September 1998, Lecture Notes in Control and Information, Vol. 249, pp. 61-87, Springer-Verlag, Berlin/Heidelberg, 1999. [ISBN: 1-85233-642-0]
DOI: 10.1007/BFb0110079
The retrievable version is NICONET Report 1999-1, Working Group on Software, January 1999.
[BC1] Numerical Methods for Linear Quadratic and H Control Problems
Peter Benner, Ralp Byers, Volker Mehrmann, and Hongguo Xu
In G. Picci and D.S. Gilliam (Eds.), Dynamical Systems, Control, Coding, Computer Vision: New Trends, Interfaces, and Interplay, Vol. 25 of Progress in Systems and Control Theory, pp. 203-222, Birkhäuser, Basel, 1999. [ISBN: 978-3-0348-9848-5]
DOI: 10.1007/978-3-0348-8970-4_10

Articles in conference proceedings

[CA196]  [new] Towards Riccati-Feedback Control of Complex Flows with Moving Interfaces
Björn Baran, Peter Benner, Jan Heiland, and Jens Saak
Proceedings in Applied Mathematics and Mechanics, Vol. 17, Issue 1, accepted 17 October 2017.
[CA195]  [new] On the Transformation Formulas of the Hankel-Norm Approximation
Peter Benner and Steffen Werner
Proceedings in Applied Mathematics and Mechanics, accepted 17 October 2017.
[CA194]  [new] Construction of a Lyapunov Functional for a Class of Controlled Population Balance Models
Alexander Zuyev, Achim Kienle, and Peter Benner
Proceedings in Applied Mathematics and Mechanics, accepted 10 October 2017.
[CA193]  [new] A Greedy Subspace Method for Computing the L>-Norm
Nicat Aliyev, Peter Benner, Emre Mengi, Paul Schwerdtner, and Matthias Voigt
Proceedings in Applied Mathematics and Mechanics, accepted 10 October 2017.
[CA192]  [new] Nonlinear Stabilizing Feedback Design for Incompressible Flows Via Updated Riccati-Based Gains
Jan Heiland and Peter Benner
56th IEEE Conference on Decision and Control, Melbourne, Australia, December 12-15, 2017, to appear.
[CA191]  [new] Sparse Model Order Reduction for Electro-Thermal Problems with Many Inputs
Nicodemus Banagaaya, Lihong Feng, Wim Schoenmaker, Peter Meuris, Renaud Gillon, and Peter Benner
In U. Langer, W. Amrhein, W. Zulehner (Eds.), Scientific Computing in Electrical Engineering - SCEE 2016, Mathematics in Industry, Springer International Publishing, accepted 12 August 2017.
[CA190]  [new] Solving Sparse Differential Riccati Equations on Hybrid CPU-GPU Platforms
Peter Benner, Ernesto Dufrechou, Pablo Ezzatti, Hermann Mena, Enrique S. Quintana-Ortí, and Alfredo Remón
In O. Gervasi, B. Murgante, S. Misra, G. Borruso, C. M. Torre, A.M.A.C. Rocha, D. Taniar, B. O. Apduhan E. Stankova, A. Cuzzocrea (Eds.), Computational Science and Its Applications – ICCSA 2017, Proceedings, Part I, Lecture Notes in Computer Science, Vol. 10404, pp. 116-132, Springer International Publishing, 2017.
DOI: 10.1007/978-3-319-62392-4_9
[CA189] Studying mixed precision techniques for the solution of algebraic Riccati equations
Peter Benner, Ernesto Dufrechou, Pablo Ezzatti, and Alfredo Remón
In 2nd Workshop on Power-Aware Computing, Ringberg Castle, July 5-8, 2017, July 2017.
DOI: 10.5281/zenodo.815496
[CA188] GPU-accelerated implementation of the storage-efficient QR decomposition
Peter Benner, Martin Köhler, and Carolin Penke
In 2nd Workshop on Power-Aware Computing, Ringberg Castle, July 5-8, 2017, July 2017.
DOI: 10.5281/zenodo.815816
[CA187] Parameterized Frequency-dependent Balanced Truncation for Model Order Reduction of Linear Systems
Xin Du and Peter Benner
In 2017 29th Chinese Control And Decision Conference (CCDC), pp. 901-908, 2017.
DOI: 10.1109/CCDC.2017.7978648
[CA186]  [new] Convergence of Approximations to Riccati-based Boundary-feedback Stabilization of Laminar Flows
Peter Benner and Jan Heiland
In IFAC World Congress 2017, Toulouse, to appear.
[CA185] Simulation gekoppelter Baugruppen: Effiziente Zeitintegrationsverfahren und Modellordnungsreduktion
Norman Lang, Peter Benner, Andreas Naumann, Jörg Wensch
In C. Brecher (Ed.), Tagungsband des 5. Kolloquiums zum SFB/TR 96, Thermo-Energetische Gestaltung von Werkzeugmaschinen - Modellierung und Simulation -, pp. 18-32, 2017. [ISBN: 978-3-86780-516-2]
[CA184] Parametric Model Order Reduction for Electro-Thermal Coupled Problems with Many Inputs
Nicodemus Banagaaya, Peter Benner, and Lihong Feng
In P. Quintela, P. Barral, D. Gómez, F.J. Pena, J. Rodríguez, P. Salgado, M.E. Vázquez-Mendéz (Eds.), Progress in Industrial Mathematics at ECMI 2016, Mathematics in Industry, Vol. 26, Springer International Publishing, 2017, accepted 19 December 2016. [ISBN: 978-3-319-63081-6]
DOI: 10.1007/978-3-319-63082-3
[CA183] Reduced-Order Modeling of Index-1 Vibrational Systems Using Interpolatory Projections
Peter Benner, Jens Saak, and M. Monir Uddin
In Proceedings of the 19th International Conference on Computer and Information Technology, December 18-20, 2016, North South University, Dhaka, Bangladesh, pp. 134-138, IEEE Publications, 2016.
[ISBN: 978-1-5090-4090-2] DOI: 10.1109/ICCITECHN.2016.7860183
[CA182] Improved Balancing for General and Structured Eigenvalue Problems
Vasile Sima and Peter Benner
In E. Petre, M. Brezovan, Proceedings of the 2016 20th International Conference on System Theory, Control and Computing (ICSTCC), October 13-15, Sinaia, Romania, pp. 381-386, IEEE, 2016.
[ISBN: 978-1-5090-2720-0] DOI: 10.1109/ICSTCC.2016.7790695
[CA181] Stability Preserving Model Reduction for Linearly Coupled Linear Time-Invariant Systems
Peter Benner, Sara Grundel, and Petar Mlinarić
Proceedings in Applied Mathematics and Mechanics, Vol. 16, pp. 817-818, 2016.
DOI: 10.1002/pamm.201610397
[CA180] Numerical Solution to Low Rank Perturbed Lyapunov Equations by the Sign Function Method
Peter Benner and Jonas Denißen
Proceedings in Applied Mathematics and Mechanics, Vol. 16, pp. 723-724, 2016.
DOI: 10.1002/pamm.201610350
[CA179] Local Steering Problem for a Class of Control-Affine Systems with Application to Continuous Crystallization Processes
Alexander Zuyev and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 16, pp. 831-832, 2016.
DOI: 10.1002/pamm.201610404
[CA178] Tuning the Blocksize for Dense Linear Algebra Factorization Routines with the Roofline Model
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, Alfredo Remón, and Juan Pablo Silva
In J. Carretero et al (Eds.), Algorithms and Architectures for Parallel Processing. ICA3PP 2016 Collocated Workshops: SCDT, TAPEMS, BigTrust, UCER, DLMCS, Granada, Spain, December 14-16, 2016, Proceedings, Lecture Notes in Computer Science, Vol. 10049, pp. 18-29, 2016.
DOI: 10.1007/978-3-319-49956-7_2
[CA177] Nonlinear Model Order Reduction for Catalytic Tubular Reactors
Jens Bremer, Pawan Goyal, Lihong Feng, Peter Benner, and Kai Sundmacher
Proceedings of the 26th Symposium on Computer Aided Process Engineering (ESCAPE), Portorož, Slovenia, 12 -15 June 2016, pp. 2373-2378, 2016.
DOI: 10.1016/B978-0-444-63428-3.50400-8
[CA176] Robust Stabilization of Laminar Flows in Varying Flow Regimes
Peter Benner and Jan Heiland
2nd IFAC Workshop on Control of Systems Governed by Partial Differential Equations (CPDE 2016), 13 — 15 June 2016, Bertinoro, Italy, IFAC-PapersOnLine, Vol. 49, Issue 8, pp. 31-36, 2016.
DOI: 10.1016/j.ifacol.2016.07.414
[CA175] Model Order Reduction for Nanoelectronics Coupled Problems with Many Inputs
Nicodemus Banagaaya, Lihong Feng, Wim Schoenmaker, Peter Meuris, Aarnout Wieers, Renaud Gillon, and Peter Benner
Proceedings of the 2016 Design, Automation & Test in Europe Conference & Exhibition (DATE), 14 – 18 March 2016, ICC, Dresden, Germany , pp. 313-318, 2016. [ISBN: 978-3-9815370-6-2]
[CA174] Algebraic Gramians for Quadratic-Bilinear Systems and their Application in Model Order Reduction
Peter Benner and Pawan Goyal
Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems - MTNS 2016, 12 - 15 July 2016, Minnesota, USA, pp. 81-83, 2016.
[CA173] Clustering-Based Model Order Reduction for Multi-Agent Systems with General Linear Time-Invariant Agents
Petar Mlinarić, Sara Grundel, and Peter Benner
Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems - MTNS 2016, 12 - 15 July 2016, Minneapolis, USA, pp. 230-235, 2016.
[CA172] An Iterative Model Order Reduction Scheme for a Special Class of Bilinear Descriptor Systems Appearing in Constraint Circuit Simulation
Pawan Goyal and Peter Benner
In M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris (Eds.), Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering, pp. 4196-4212, 2016.
[CA171] Reduced Basis Method for Poisson-Boltzmann Equation
Cleophas Kweyu, Martin W. Hess, Lihong Feng, Matthias Stein, and Peter Benner
In M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris (Eds.), Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering, pp. 4187-4195, 2016.
[CA170] Time-Varying Stabilization of a Class of Driftless Systems Satisfying Second-Order Controllability Condition
Alexander Zuyev, Victoria Grushkovskaya, and Peter Benner
Proceedings of 2016 European Control Conference (ECC), 29 June - 1 July, 2016. Aalborg, Denmark, pp. 575-580, 2016.
DOI: 10.1109/ECC.2016.7810346
[CA169] Berechnung von thermo-elastischen Deformationen in Werkzeugmaschinen - Vergleich numerischer Verfahren
Michael Beitelschmidt, Peter Benner, Norman Lang, Andreas Naumann, Marian Partzsch, Axel Voigt, and Jörg Wensch
In C. Brecher (Ed.), Tagungsband des 4. Kolloquiums zum SFB/TR 96, Thermo-Energetische Gestaltung von Werkzeugmaschinen, pp. 83-95, Verlag Wissenschaftliche Scripten, 2016. [ISBN: 978-3-95735-038-1]
[CA168] Output Error Estimates in Reduced Basis Methods for Time-Harmonic Maxwell's Equations
Martin W. Hess and Peter Benner
In B. Karasözen, M. Manguoglu, M. Tezer-Sezgin, S. Göktepe, and Ö. Ugur (Eds.), Numerical Mathematics and Advanced Applications - ENUMATH 2015, Lecture Notes in Computational Science and Engineering, Vol. 112, pp. 351-358, 2016.
DOI: 10.1007/978-3-319-39929-4_33
[CA167] Efficient Model Order Reduction for Multi-Agent Systems Using QR Decomposition-Based Clustering
Petar Mlinarić, Sara Grundel, and Peter Benner
Proceedings of the 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, Dec. 2015, pp. 4794-4799, 2015.
DOI: 10.1109/CDC.2015.7402967
[CA166] A New Interpolatory Model Reduction Approach for Quadratic Bilinear Descriptor Systems
Mian Ilyas Ahmad, Peter Benner, and Lihong Feng
Proceedings in Applied Mathematics and Mechanics, Vol. 15, pp. 589-590, 2015.
DOI: 10.1002/pamm.201510284
[CA165] Exploring the Offload Execution in the Intel Xeon Phi via Matrix Inversion
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
In G. R. Joubert et al. (Eds.), Parallel Computing: On the Road to Exascale, Advances in Parallel Computing, Vol. 27, pp. 237-246, 2016. [ISBN: 978-1-61499-620-0]
DOI: 10.3233/978-1-61499-621-7-237
[CA164] A Parallel Multi-Threaded Solver for Symmetric Positive Definite Bordered-Band Linear Systems
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
In R. Wyrzykowski et al. (Eds.), Parallel Processing and Applied Mathematics - PPAM 2015, Lecture Notes in Computer Science, Vol. 9573, pp. 96-105, 2016.
DOI: 10.1007/978-3-319-32149-3_10
[CA163] Revisiting the Gauss-Huard Algorithm for the Solution of Linear Systems on Graphics Accelerators
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
In R. Wyrzykowski et al. (Eds.), Parallel Processing and Applied Mathematics - PPAM 2015, Lecture Notes in Computer Science, Vol. 9573, pp. 505-514, 2016.
DOI: 10.1007/978-3-319-32149-3_47
[CA162] Solving Dense Linear Systems with Hybrid ARM+GPU Platforms[in Spanish]
Juan P. Silva, Ernesto Dufrechou, Pablo Ezzatti, Enrique S. Quintana-Ortí, Peter Benner, and Alfredo Remón
Proceedings of the 41st Latin American Computing Conference - CLEI 2015, 19-23 October 2015. Arequipa, Peru, pp. 1-8, 2015.
DOI: 10.1109/CLEI.2015.7360027
[CA161] Reduced Basis Modeling for Uncertainty Quantification of Electromagnetic Problems in Stochastically Varying Domains
Peter Benner and Martin W. Hess
In A. Bartel, M. Clemens, M. Günther, E. J. W. ter Maten (Eds.), Scientific Computing in Electrical Engineering - SCEE 2014, Mathematics in Industry, Vol. 23, pp. 215-222, 2016.
DOI: 10.1007/978-3-319-30399-4_21
[CA160] Parametric and Reduced-Order Modeling for the Thermal Analysis of Nanoelectronic Structures
Lihong Feng, Peter Meuris, Wim Schoenmaker, and Peter Benner
In A. Bartel, M. Clemens, M. Günther, E. J. W. ter Maten (Eds.), Scientific Computing in Electrical Engineering - SCEE 2014, Mathematics in Industry, Vol. 23, pp. 155-163, 2016.
DOI: 10.1007/978-3-319-30399-4_16
[CA159] Approximation and Model Order Reduction for Second Order Systems with Levy-Noise
Martin Redmann and Peter Benner
Dynamical Systems, Differential Equations and Applications. AIMS Proceedings, pp. 945-953, 2015.
DOI: 10.3934/proc.2015.0945
[CA158] An Efficient Output Error Bound for Model Order Reduction of Parametrized Evolution Equations
Yongjin Zhang, Lihong Feng, Suzhou Li, and Peter Benner
8th Vienna International Conference on Mathematical Modelling MATHMOD 2015, 18-20 February, 2015. Vienna, Austria, IFAC-PapersOnLine, Vol. 48, pp. 9-10, 2015.
DOI: 10.1016/j.ifacol.2015.05.096
[CA157] Model Order Reduction of an Electro-Thermal Package Model
Nicodemus Banagaaya, Lihong Feng, Peter Meuris, Wim Schoenmaker, and Peter Benner
8th Vienna International Conference on Mathematical Modelling MATHMOD 2015, 18-20 February, 2015. Vienna, Austria, IFAC-PapersOnLine, Vol. 48, pp. 934-935, 2015.
DOI: 10.1016/j.ifacol.2015.05.212
[CA156] Model Reduction of Quadratic-Bilinear Descriptor Systems via Carleman Bilinearization
Pawan Kumar Goyal, Mian Ilyas Ahmad, and Peter Benner
Proceedings of 2015 European Control Conference (ECC), 15-17 July, 2015. Linz, Austria, pp. 1177-1182, 2015.
DOI: 10.1109/ECC.2015.7330699
[CA155] Solving SLICOT Benchmarks for Continuous-time Algebraic Riccati Equations by Hamiltonian Solvers
Vasile Sima and Peter Benner
Proceedings of the 19th International Conference on System Theory, Control and Computing, 14-16 October, 2015. Cheile Gradistei - Fundata Resort, Romania, pp. 1-6, 2015.
DOI: 10.1109/ICSTCC.2015.7321260
[CA154] Pitfalls when Solving Eigenproblems with Applications in Control Engineering
Vasile Sima and Peter Benner
Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2015), 21-23 July, 2015. Colmar, France, Vol. 1, pp. 171-178, 2015.
DOI: 10.5220/0005533301710178
[CA153] Ehrlich-Aberth Iteration For Vibrational Systems
Peter Benner and Jonas Denißen
Proceedings of the IFTOMM International Conference on Engineering Vibration 2015 (ICoEV 2015), Ljubljana, Slovenia, pp. 1540-1548, 2015.
[CA152] Application of Krylov-type Parametric Model Order Reduction in Efficient Uncertainty Quantification of Electro-thermal Circuit Models
Yao Yue, Lihong Feng, Peter Meuris, Wim Schoenmaker, and Peter Benner
Proceedings of the Progress In Electromagnetics Research Symposium (PIERS 2015), Prague, Czech Republic, pp. 379-384, 2015.
DOI: 10.17617/2.2223025
[CA151] Automatic Generation of Reduced Order Models for Linear Parametric Systems
Lihong Feng, Athanasios C. Antoulas, and Peter Benner
In G. Russo, V. Capasso, G. Nicosia, and V. Romano (Eds.), Progress in Industrial Mathematics at ECMI 2014, Mathematics in Industry, Vol. 22, Springer International Publishing, 2016. [ISBN: 978-3-319-23412-0].
DOI: 10.1007/978-3-319-23413-7
[CA150] Distributed Optimal Control Problems Governed by Coupled Convection Dominated PDEs with Control Constraints
Hamdullah Yücel and Peter Benner
In A. Abdulle, S. Deparis, D. Kressner, F. Nobile, and M. Picasso (Eds.), Numerical Mathematics and Advanced Applications - ENUMATH 2013, Lecture Notes in Computational Science and Engineering, Vol. 103, pp. 469-478, Springer International Publishing, 2015. [ISBN: 978-3-319-10704-2]
DOI: 10.1007/978-3-319-10705-9_46
[CA149] Reduced-Order Modeling and ROM-Based Optimization of Batch Chromatography
Peter Benner, Lihong Feng, Suzhou Li, and Yongjin Zhang
In A. Abdulle, S. Deparis, D. Kressner, F. Nobile, and M. Picasso (Eds.), Numerical Mathematics and Advanced Applications - ENUMATH 2013, Lecture Notes in Computational Science and Engineering, Vol. 103, pp. 427-435, Springer International Publishing, 2015. [ISBN: 978-3-319-10704-2]
DOI: 10.1007/978-3-319-10705-9_42
[CA148] Mapping Parameters Across System Boundaries: Parameterized Model Reduction with Low Rank Variability in Dynamics
Ulrike Baur, Christopher Beattie, and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 14, pp. 19–22, 2014.
DOI: 10.1002/pamm.201410006
[CA147] A Cache-Aware Implementation of the Spectral Divide-and-Conquer Approach for the Non-Symmetric Generalized Eigenvalue Problem
Peter Benner, Martin Köhler, and Jens Saak
Proceedings in Applied Mathematics and Mechanics, Vol. 14, Issue 1, pp. 819–820, 2014.
DOI: 10.1002/pamm.201410390
[CA146] Spectral Bounds on the Solution of Linear Time-Periodic Systems
Peter Benner and Jonas Denißen
Proceedings in Applied Mathematics and Mechanics, Vol. 14, Issue 1, pp. 863–864, 2014.
DOI: 10.1002/pamm.201410412
[CA145] Generalized Inverses of Periodic Matrix Pairs and Model Reduction for Periodic Control Systems
Mohammad-Sahadet Hossain and Peter Benner
In Proceedings of the 2014 International Conference on Electrical Engineering and Information & Communication Technology (ICEEICT), pp. 1-6, IEEE Publications, 2014. [ISBN: 978-1-4799-4820-8]
DOI: 10.1109/ICEEICT.2014.6919033
[CA144] Interpolatory Model Reduction Techniques for Linear Second-Order Descriptor Systems
Mian Ilyas Ahmad and Peter Benner
Proceedings of 2014 European Control Conference (ECC), pp. 1075-1079, IEEE Publications, 2014.
DOI: 10.1109/ECC.2014.6862210
[CA143] Accelerating Band Linear Algebra Operations on GPUs with Application in Model Reduction
Peter Benner, Ernesto Dufrechou, Pablo Ezzatti, Pablo Igounet, Enrique S. Quintana-Ortí, and Alfredo Remón
In B. Murgante et al (Eds.), Computational Science and Its Applications – ICCSA 2014 14th International Conference, Guimarães, Portugal, June 30 – July 3, 2014, Proceedings, Part VI, Lecture Notes in Computer Science, Vol. 8584, pp. 386-400, Springer International Publishing, 2014.
DOI: 10.1007/978-3-319-09153-2_29
[CA142] Accelerating the General Band Matrix Multiplication Using Graphics Processors
Peter Benner, Alfredo Remón, Ernesto Dufrechou, Pablo Ezzatti, and Enrique S. Quintana-Ortí
Proceedings of XL Conferencia Lationamericana en Informática. Montevideo (Uruguay), pp. 1-7, 2014.
DOI: 10.1109/CLEI.2014.6965142
[CA141] Numerical Investigation of Newton’s Method for Solving Continuous-time Algebraic Riccati Equations
Vasile Sima and Peter Benner
In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO), pp. 404-409, SCITEPRESS, 2014.
DOI: 10.5220/0005117004040409.
[CA140] Efficient Solvers for Large-Scale Saddle Point Systems Arising in Feedback Stabilization of Multi-Field Flow Problems
Peter Benner, Jens Saak, Martin Stoll, and Heiko K. Weichelt
In C. Pötzsche, C. Heuberger, B. Kaltenbacher, and F. Rendl (Eds.), System Modeling and Optimization. 26th IFIP TC 7 Conference, Klagenfurt, Austria, September 8–13, 2013, IFIP AICT, Vol. 443, pp. 11-20, Springer-Verlag, Berlin/Heidelberg, 2014.
DOI: 10.1007/978-3-662-45504-3_2.
[CA139] Using Model Order Reduction to Accelerate Optimization of Multi-Stage Linear Dynamical Systems
Yao Yue, Suzhou Li, Lihong Feng, Andreas Seidel-Morgenstern, and Peter Benner
In A. Araujo (Ed.), Engineering Optimization IV, pp. 453-458, CRC Press, 2014.[ISBN: 978-1-138-02725-1]
DOI: 10.1201/b17488-80.
[CA138] Balanced Truncation for Stochastic Linear Systems with Guaranteed Error Bound
Tobias Damm and Peter Benner
In Proceedings of The 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), pp. 1492-1497, 2014.
[CA137] Efficient Model Reduction of SMB Chromatography by Krylov-subspace Method with Application to Uncertainty Quantification
Yao Yue, Suzhou Li, Lihong Feng, Andreas Seidel-Morgenstern, and Peter Benner
In J. J. Klemeš, P. S. Varbanov, and P. Y. Liew (Eds.), Proceedings of the 24th European Symposium on Computer Aided Process Engineering, Part-A, pp. 925-930, Elsevier B.V., 2014.[ISBN: 978-0-444-63456-6]
DOI: 10.1016/B978-0-444-63456-6.50155-1
[CA136] Balancing-Related Model Reduction for Parabolic Control Systems
Peter Benner
Proceedings of the 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations, IFAC-PapersOnLine, pp. 257-262, 2013.
DOI: 10.3182/20130925-3-FR-4043.00065
[CA135] Optimal Control for Allen-Cahn Equations Enhanced by Model Predictive Control
Peter Benner and Martin Stoll
Proceedings of the 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations, IFAC-PapersOnLine, pp. 139-143, 2013.
DOI: 10.3182/20130925-3-FR-4043.00062
[CA134] On the Impact of Optimization on the Time-Power-Energy Balance of Dense Linear Algebra Factorizations
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
In R. Aversa, J. Kolodziej, J. Zhang, F. Amato, F. Giancarlo (Eds.), 13th International Conference, ICA3PP 2013, Vietri sul Mare, Italy, December 18-20, 2013, Proceedings, Part I, Lecture Notes in Computer Science, Vol. 8286, pp. 3-10, Springer-Verlag, Berlin/Heidelberg, 2013.
DOI: 10.1007/978-3-319-03889-6_1
[CA133] Fast Approximate Solution of the Non-Symmetric Generalized Eigenvalue Problem on Multicore Architectures
Peter Benner, Martin Köhler, and Jens Saak
In M. Bader, A. Bode, H.-J. Bungartz, M. Gerndt, G.R. Joubert, F. Peters (Eds.), Parallel Computing: Accelerating Computational Science and Engineering (CSE). Advances in Parallel Computing, Vol. 25, pp. 143-152, IOS Press, 2014.
DOI: 10.3233/978-1-61499-381-0-143
[CA132] Exploiting Data- and Task-Parallelism in the Solution of Riccati Equations on Multicore Servers and GPUs
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
In M. Bader, A. Bode, H.-J. Bungartz, M. Gerndt, G.R. Joubert, F. Peters (Eds.), Parallel Computing: Accelerating Computational Science and Engineering (CSE). Advances in Parallel Computing, Vol. 25, pp. 367-374, IOS Press, 2014.
DOI: 10.3233/978-1-61499-381-0-367
[CA131] Trading Off Performance for Power-Energy in Dense Linear Algebra Operations
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
In Proceedings of VI Latin American Symposium on High Performance Computing - HPCLatAm 2013. Mendoza (Argentina), pp. 158-166, 2013.
[CA130] Computation of the H-Norm for Large-Scale Systems
Matthias Voigt, Peter Benner, and Ryan Lowe
Mathematisches Forschungsinstitut Oberwolfach, Vol. 10, Issue 4, pp. 3289-3291, 2013.
DOI: 10.4171/OWR/2013/56
[CA129] A Parallel, Adaptive Multi-Point Model Order Reduction Algorithm
Giovanni De Luca, Guilio Antonini, and Peter Benner
In Proceedings of 22nd Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS), pp. 115-118, 2013, IEEE Publications.
DOI: 10.1109/EPEPS.2013.6703479
[CA128] Reachability and Observability Concepts for Stochastic Systems
Peter Benner and Martin Redmann
Proceedings in Applied Mathematics and Mechanics, Vol. 13, Issue 1, pp. 381-382, 2013.
DOI: 10.1002/pamm.201310186
[CA127] A Reformulated Low-Rank ADI Iteration with Explicit Residual Factors
Peter Benner, Patrick Kürschner, and Jens Saak
Proceedings in Applied Mathematics and Mechanics, Vol. 13, Issue 1, pp. 585-586, 2013.
DOI: 10.1002/pamm.201310273
[CA126] Bounds on the Solution of Linear Time-Periodic Systems
Peter Benner, Jonas Denißen, and Ludwig Kohaupt
Proceedings in Applied Mathematics and Mechanics, Vol. 13, Issue 1, pp. 447-448, 2013.
DOI: 10.1002/pamm.201310217
[CA125] Modeling Structural Variability in Reduced Order Models of Machine Tool Assembly Groups via Parametric MOR
Peter Benner, Norman Lang, and Jens Saak
Proceedings in Applied Mathematics and Mechanics, Vol. 13, Issue 1, pp. 481-482, 2013.
DOI: 10.1002/pamm.201310233
[CA124] Modellordnungsreduktion für geschaltete, gekoppelte thermo-elastische Systeme
Peter Benner, Norman Lang, Jens Saak
In O. Sawodny and J. Adamy (Eds.), Tagungsband des GMA-Fachausschusses 1.30 Modellbildung, Identifikation und Simulation in der Automatisierungstechnik, pp. 215-227, 2013.
[CA123] Reduced Basis Generation for Maxwell’s Equations by Rigorous Error Estimation
Martin W. Hess and Peter Benner
In Proceedings of 19th International Conference on the Computation of Electromagnetic Fields (COMPUMAG 2013), Paper PD2-10 (2 pp.), 2013.
[CA122] Second Order to Second Order Balancing for Index-1 Vibrational Systems
Peter Benner, Jens Saak, and M. Monir Uddin
In Proceedings of the 2012 7th International Conference on Electrical and Computer Engineering 20-22 December, 2012, Dhaka, Bangladesh, pp. 933-936, IEEE Publications, 2012. [ISBN: 978-1-4673-1436-7]
DOI: 10.1109/ICECE.2012.6471704
[CA121] Iterative Solvers for Periodic Matrix Equations and Model Reduction for Periodic Control Systems
Mohammad-Sahadet Hossain and Peter Benner
In Proceedings of the 2012 7th International Conference on Electrical and Computer Engineering 20-22 December, 2012, Dhaka, Bangladesh, pp. 791-794, IEEE Publications, 2012. [ISBN: 978-1-4673-1436-7]
DOI: 10.1109/ICECE.2012.6471669
[CA120] H-Norm Computation for Large and Sparse Descriptor Systems
Peter Benner and Matthias Voigt
Proceedings in Applied Mathematics and Mechanics, Vol. 12, Issue 1, pp. 797–800, 2012.
DOI: 10.1002/pamm.201210383
[CA119] Avoiding Complex Arithmetic in the Low-Rank ADI Method Efficiently
Peter Benner, Patrick Kürschner, and Jens Saak
Proceedings in Applied Mathematics and Mechanics, Vol. 12, Issue 1, pp. 639–640, 2012.
DOI: 10.1002/pamm.201210308
Extendend version available as MPI Magdeburg Preprint MPIMD/12-11, May 2012.
[CA118] The Reduced Basis Method for Time-Harmonic Maxwell's Equations
Peter Benner and Martin W. Hess
Proceedings in Applied Mathematics and Mechanics, Vol. 12, Issue 1, pp. 661–662, 2012.
DOI: 10.1002/pamm.2012319
[CA117] Efficient Reduced Order State Space Model Computation for a Class of Second Order Index One Systems
Peter Benner, Burkhard Kranz, Jens Saak, and M. Monir Uddin
Proceedings in Applied Mathematics and Mechanics, Vol. 12, Issue 1, pp. 699–700, 2012.
DOI: 10.1002/pamm.2012338
[CA116] MPC/LQG for Infinite-Dimensional Systems Using Time-Invariant Linearizations
Peter Benner and Sabine Hein
In System Modeling and Optimization. 25th IFIP TC 7 Conference, Berlin, Germany, September 12-16, 2011, Revised Selected Papers, IFIP AICT, Vol. 391, pp. 217-224, Springer-Verlag, Berlin/Heidelberg, 2013. [ISBN 978-3-642-36061-9]
DOI: 10.1007/978-3-642-36062-6_22
[CA115] Numerical Computation of Structured Complex Stability Radii of Large-Scale Matrices and Pencils
Peter Benner and Matthias Voigt
In Proceedings of the 51st IEEE Conference on Decision and Control, December 10-13, 2012, Maui, HI, USA, pp. 6560-6565, IEEE Publications, 2012. [ISBN: 978-1-4673-2064-1]
© IEEE. DOI: 10.1109/CDC.2012.6426906
[CA114] High Performance Implementations of the BST Method on Hybrid CPU-GPU Platforms
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
In Proceedings of the 10th IEEE International Symposium on Parallel and Distributed Processing with Applications, Leganés, Madrid, 10-13 July 2012, IEEE Publications, pp. 662-668, 2012.
DOI: 10.1109/ISPA.2012.98
[CA113] New SLICOT Routines Based on Structured Eigensolvers (author's version)
Peter Benner, Daniel Kressner, and Vasile Sima
In Proceedings of the 2012 IEEE Multi-Conference on Systems and Control, October 3-5, 2012. Dubrovnik, Croatia, pp. 640-645, IEEE Publications, 2012.
DOI: 10.1109/CCA.2012.6402437
© IEEE.
[CA112] Structure Preserving Iterative Solution of Periodic Projected Lyapunov Equations
Peter Benner and Mohammad-Sahadet Hossain
In Proceedings of MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, IFAC-PapersOnLine, Mathematical Modelling, Vol. 7, Part 1, pp. 276-281, 2012.
DOI: 10.3182/20120215-3-AT-3016.00048
[CA111] A Goal-Oriented Dual LRCF-ADI for Balanced Truncation
Jens Saak, Peter Benner, and Patrick Kürschner
In Proceedings of MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, IFAC-PapersOnLine, Mathematical Modelling, Vol. 7, Part 1, pp. 752-757, 2012.
DOI: 10.3182/20120215-3-AT-3016.00133
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/12-01, January 2012.
[CA110] Improved Second-Order Balanced Truncation for Symmetric Systems
Peter Benner, Patrick Kürschner, and Jens Saak
In Proceedings of MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, IFAC-PapersOnLine, Mathematical Modelling, Vol. 7, Part 1, pp. 758-762, 2012.
DOI: 10.3182/20120215-3-AT-3016.00134
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/11-13, December 2011.
[CA109] Robust and Efficient Algorithms for L-Norm Computation for Descriptor Systems
Peter Benner, Vasile Sima, and Matthias Voigt
In Proceedings of 7th IFAC Symposium on Robust Control Design, Aalborg, Denmark, June 20-22, 2012, Vol. 45, Issue 13, pp. 195-200, 2012.
DOI: 10.3182/20120620-3-DK-2025.00114
[CA108] Efficient Optimization of Simulated Moving Bed Processes Using Reduced Order Models
Suzhou Li, Lihong Feng, Peter Benner, and Andreas Seidel-Morgenstern
In I. D. Lockhart Bogle and M. Fairweather (Eds.), Proceedings of the 22nd European Symposium on Computer Aided Process Engineering, Part-B, Vol. 30, pp. 1232-1236, Elsevier B.V., 2012. [ISBN: 978-0-444-59520-1]
DOI: 10.1016/B978-0-444-59520-1.50105-6
[CA107] L-Norm Computation for Discrete-Time Descriptor Systems
Peter Benner and Matthias Voigt
In O. Sawodny and J. Adamy (Eds.), Tagungsband GMA-FA 1.30 "Modellbildung, Identifizierung und Simulation in der Automatisierungstechnik", Workshops in Anif, 21.-23. September 2011, pp. 228-240, 2011. [ISBN: 978-3-9815012-1-6]
[CA106] On H2-Model Reduction of Linear Parameter-Varying Systems
Peter Benner and Tobias Breiten
Proceedings in Applied Mathematics and Mechanics, Vol. 11, Issue 1, pp. 805–806, 2011.
DOI: 10.1002/pamm.201110391
[CA105] Two-sided Harmonic Subspace Extractions for the Generalized Eigenvalue Problem
Peter Benner, Michiel Hochstenbach, and Patrick Kürschner
Proceedings in Applied Mathematics and Mechanics, Vol. 11, Issue 1, pp.739–740, 2011.
DOI: 10.1002/pamm.201110359
[CA104] Locally Optimal Block Preconditioned Conjugate Gradient Method for Hierarchical Matrices
Peter Benner and Thomas Mach
Proceedings in Applied Mathematics and Mechanics, Vol. 11, Issue 1, pp. 741–742, 2011.
DOI: 10.1002/pamm.201110360
[CA103] On the Computation of Particular Eigenvectors of Hamiltonian Matrix Pencils
Peter Benner and Matthias Voigt
Proceedings in Applied Mathematics and Mechanics, Vol. 11, Issue 1, pp. 753–754, 2011.
DOI: 10.1002/pamm.201110366
[CA102] Accelerating BST Methods for Model Reduction with Graphics Processors
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
In Parallel Processing and Applied 9th International Conference, PPAM 2011, Torun, Poland, September 11-14, 2011. Revised Selected Papers, Part I, Lecture Notes in Computer Science, Vol. 7203, pp. 549-558, Springer-Verlag, Berlin/Heidelberg, 2012.
DOI: 10.1007/978-3-642-31464-3_56
[CA101] High Performance Matrix Inversion of SPD Matrices on Graphics Processors
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
In W. W. Smari (Ed.), Proceedings of the 2011 International Conference on High Performance Computing & Simulation (HPCS 2011), pp. 640-646, IEEE Publications, 2011. [ISBN: 978-1-61284-382-7]
DOI: 10.1109/HPCSim.2011.5999887
[CA100] Krylov-Subspace Based Model Reduction of Nonlinear Circuit Models Using Bilinear and Quadratic-Linear Approximations
Peter Benner and Tobias Breiten
In M. Günther, A. Bartel, M. Brunk, S. Schöps, M. Striebel (Eds.), Progress in Industrial Mathematics at ECMI 2010, Mathematics in Industry, Vol. 17, pp. 153-159, Springer-Verlag, Berlin, 2012. [ISBN 978-3-642-25099-6]
DOI: 10.1007/978-3-642-25100-9_18
[CA99] Model Reduction for Linear Descriptor Systems with Many Ports
Peter Benner und André Schneider
In M. Günther, A. Bartel, M. Brunk, S. Schöps, M. Striebel (Eds.), Progress in Industrial Mathematics at ECMI 2010, Mathematics in Industry, Vol. 17, pp. 137-143, Springer-Verlag, Berlin, 2012. [ISBN 978-3-642-25099-6]
DOI: 10.1007/978-3-642-25100-9_16
[CA98] Some Remarks on A Priori Error Estimation for ESVDMOR
Peter Benner and André Schneider
In B. Michielsen and J.-R. Poirier (Eds.), Scientific Computing in Electrical Engineering SCEE 2010, Mathematics in Industry, Vol. 16, pp. 15-23, Springer-Verlag, Berlin, 2012. [ISBN 978-3-642-22452-2]
DOI: 10.1007/978-3-642-22453-9_2
[CA97] Damping Optimization for Linear Vibrating Systems Using Dimension Reduction
Peter Benner, Zoran Tomljanović, and Ninoslav Truhar
In J. Náprstek, J. Horáček, M. Okrouhlík, B. Marvalová, F. Verhulst, and J.T. Sawicki (Eds.), Vibration Problems ICOVP 2011. The 10th International Conference on Vibration Problems, Springer Proceedings in Physics, Vol. 139, Springer-Verlag, pp. 297-305, 2011. [ISBN: 978-94-007-2068-8]
DOI: 10.1007/978-94-007-2069-5_41
[CA96] Accelerating Model Reduction of Large Linear Systems with Graphics Processors
Peter Benner, Pablo Ezzatti, Daniel Kressner, Enrique S. Quintana-Ortí, and Alfredo Remón
In K. Jónasson (Ed.), Applied Parallel and Scientific Computing. 10th International Conference, PARA 2010, Reykjavík, Iceland, June 6-9, 2010, Revised Selected Papers, Part II, Lecture Notes in Computer Science, Vol. 7134, pp. 88-97, Springer-Verlag, Berlin/Heidelberg, 2012. [ISBN 978-3-642-28144-0]
DOI: 10.1007/978-3-642-28145-7_9
[CA95] Solving Differential Riccati Equations on Multi-GPU Platforms
Peter Benner, Pablo Ezzatti, Hermann Mena, Enrique S. Quintana-Ortí, and Alfredo Remón
In J. Vigo-Aguilar (Ed.), Proceedings of the 11th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2011, Vol. 1, pp. 178-188, 2011. [ISBN: 978-84-614-6167-7]
[CA94] Modern Model Reduction of Elastic Components for the Simulation og flexible Multibody Systems [in German]
Christine Nowakowski, Peter Eberhard, Patrick Kürschner, Peter Benner, Gerald Ochse, and Gunter Knoll
In Tagungsband zur FVV Frühjahrstagung 2011, Forschungsvereinigung Verbrennungskraftmaschinen e.V., Frankfurt a.M., Issue R553, pp. 175-197, 2011.
[CA93] Model Order Reduction of Large-Scale Dynamical Systems with Jacobi-Davidson Style Eigensolvers
Peter Benner, Michiel E. Hochstenbach, and Patrick Kürschner
In Proceedings of the 2011 International Conference on Communications, Computing and Control Applications (CCCA’11), March 3-5, 2011 at Hammamet, Tunisia, IEEE Publications (6 pages), 2011.
DOI: 10.1109/CCCA.2011.6031208
[CA92] Modern Methods for Model Order Reduction of Finite Element Models for the Simulation of Machine Tools [in German]
Thomas Bonin, Andreas Soppa, Jens Saak, Michael Zäh, Heike Faßbender, and Peter Benner
In T. Bertram and B. Corves (Eds.), Tagungsband der VDI-Fachtagung Mechatronik 2011, 31.3-1.4.2011, Dresden, pp. 333-338, TU Dresden, 2011. [ISBN: 978-3-00-033892-2]
[CA91] Suboptimality Estimates for the Semi-Discretized LQR Problem for Parabolic PDEs
Peter Benner and Jens Saak
Proceedings in Applied Mathematics and Mechanics, Vol. 10, Issue 1, pp. 591–592, 2010.
DOI: 10.1002/pamm.201010288.
[CA90] Krylov Subspace Methods for Model Order Reduction of Bilinear Discrete-Time Control Systems
Peter Benner, Tobias Breiten, and Tobias Damm
Proceedings in Applied Mathematics and Mechanics, Vol. 10, pp. 601-602, 2010.
DOI: 10.1002/pamm.201010293.
[CA89] Nonlinear Model Order Reduction via Quadratic Bilinear Differential Algebraic Equations
Tobias Breiten and Peter Benner
In B. Lohmann and A. Kugi (Eds.), Tagungsband GMA-FA 1.30 "Modellbildung, Identifizierung und Simulation in der Automatisierungstechnik", Workshops in Anif, 22.-24. September 2010, pp. 138-153, 2010. [ISBN: 978-3-9502451-7-2]
[CA88] On Stability, Passivity and Reciprocity Preservation of ESVDMOR
Peter Benner and André Schneider
In P. Benner, M. Hinze, E. Jan W. ter Maten (Eds.), Model Reduction for Circuit Simulation, Lecture Notes in Electrical Engineering, Vol. 74, pp. 277-288, Springer-Verlag, Dordrecht, 2011. [ISBN: 978-94-007-0088-8]
DOI: 0.1007/978-94-007-0089-5_16.
[CA87] Recycling Krylov Subspaces for Solving Linear Systems with Successively Changing Right-hand Sides Arising in Model Reduction
Peter Benner and Lihong Feng
In P. Benner, M. Hinze, E. Jan W. ter Maten (Eds.), Model Reduction for Circuit Simulation, Lecture Notes in Electrical Engineering, Vol. 74, pp. 125-140, Springer-Verlag, Dordrecht, 2011. [ISBN: 978-94-007-0088-8]
DOI: 10.1007/978-94-007-0089-5_6.
[CA86] Balanced Truncation Model Order Reduction for LTI Systems with many Inputs or Outputs
Peter Benner and André Schneider
In András Edelmayer (Ed.), Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), 5-9 July, 2010, Budapest, Hungary, pp. 1971-1974, 2010. [ISBN: 978-963-311-370-7]
[CA85] Numerical Solution of Differential Riccati Equations on Hybrid CPU-GPU Platforms
Peter Benner, Pablo Ezzatti, Hermann Mena, Enrique S. Quintana-Ortí, and Alfredo Remón
In Proceedings of ALAMA2010 - 2nd Meeting on Linear Algebra, Matrix Analysis, and Applications, Valencia, June 2nd-4th, 2010, 7 pages, 2010. [ISBN: 978-84-8363-544-5]
[CA84] H Control for Descriptor Systems - a Pencil Based Approach
Peter Benner and Philip Losse
Proceedings in Applied Mathematics and Mechanics, Vol. 9, pp. 645-646, 2009.
DOI: 10.1002/pamm.200910292.
[CA83] b>Computing the Eigenvalues of Hierarchical Matrices by LR-Cholesky Transformations
Peter Benner and Thomas Mach
Mathematisches Forschungsinstitut Oberwolfach, Report No. 37/2009, pp. 2107-2109, 2009.
DOI: 10.4171/OWR/2009/37.
[CA82] Model Reduction of Periodic Descriptor Systems Using Balanced Truncation
Peter Benner, Mohammad-Sahadet Hossain, and Tatjana Stykel
In P. Benner, M. Hinze, E. Jan W. ter Maten (Eds.) Model Reduction for Circuit Simulation, Lecture Notes in Electrical Engineering, Vol. 74, pp. 193-206, Springer-Verlag, Dordrecht, 2011.
DOI: 10.1007/978-94-007-0089-5_11.
Note: This is a corrected version, there is a typo on p. 196 in the book: In the definition of Pr(k), nk+1 should be nk!
[CA81] Novel Model Reduction Techniques for Control of Machine Tools
Peter Benner, Thomas Bonin, Heike Faßbender, Jens Saak, Andreas Soppa, and Michael Zaeh
In Proceedings of the ANSYS Conference & 27. CADFEM Users' Meeting 2009, 18.-20. November 2009, Congress Center Leipzig, paper 2.9.18 (10 pages), 2009.
[CA80] Using Hybrid CPU-GPU Platforms to Accelerate the Computation of the Matrix Sign Function
Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, and Alfredo Remón
In H.-X. Lin, M. Alexander, M. Forsell, A. Knüpfer, R. Prodan, L. Sousa, and A. Streit (Eds.) Euro-Par 2009, Parallel Processing - Workshops., Lecture Notes in Computer Science, Vol. 6043, pp. 132-139, Springer-Verlag, Berlin/Heidelberg, 2010.
DOI: 10.1007/978-3-642-14122-5_17.
[CA79] Model Predictive Control for Nonlinear Parabolic Differential Equations Based on a Linear Quadratic Gaussian Design
Peter Benner and Sabine Hein
Proceedings in Applied Mathematics and Mechanics, Vol. 9, pp. 613-614, 2009.
DOI: 10.1002/pamm.200910278.
[CA78] Parametric Model Order Reduction Accelerated by Subspace Recycling
Lihong Feng, Peter Benner, and Jan G. Korvink
In Proceedings of 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, P.R. China, December 16-18, 2009, pp. 4328-4333, 2009.
DOI: 10.1109/CDC.2009.5399717.
[CA77] System-Theoretic Methods for Model Reduction of Large-Scale Systems: Simulation, Control, and Inverse Problems
Peter Benner
In I. Troch and F. Breitenecker (Eds.), Proceedings of MathMod 2009, Vienna, February 11-13, 2009, ARGESIM Report no. 35, pp. 126-145, 2009. [ISBN: 978-3-901608-35-3]
[CA76] Efficient Balancing based MOR for Second Order Systems Arising in Control of Machine Tools
Peter Benner and Jens Saak
In I. Troch and F. Breitenecker (Eds.), Proceedings of MathMod 2009, Vienna, February 11-13, 2009, ARGESIM Report no. 35, pp. 1232-1243, 2009. [ISBN: 978-3-901608-35-3]
[CA75] Advances in Balancing-Related Model Reduction for Circuit Simulation
Peter Benner
In J. Roos and L.R.J. Costa (Eds.), Scientific Computing in Electrical Engineering SCEE 2008, Mathematics in Industry, Vol. 14, pp. 469-482, Springer-Verlag, Berlin/Heidelberg, 2010.
DOI: 10.1007/978-3-642-12294-1_58.
[CA74] Model Order and Terminal Reduction Approaches via Matrix Decomposition and Low Rank Approximation
Peter Benner and André Schneider
In J. Roos and L.R.J. Costa (Eds.), Scientific Computing in Electrical Engineering SCEE 2008, Mathematics in Industry, Vol. 14, pp. 523-530, Springer-Verlag, Berlin/Heidelberg, 2010.
DOI: 10.1007/978-3-642-12294-1_64.
[CA73] Model Order Reduction for Systems with Non-Rational Transfer Function Arising in Computational Electromagnetics
Lihong Feng and Peter Benner
In J. Roos and L.R.J. Costa (Eds.), Scientific Computing in Electrical Engineering SCEE 2008, Mathematics in Industry, Vol. 14, pp. 515-522, Springer-Verlag, Berlin/Heidelberg, 2010.
DOI: 10.1007/978-3-642-12294-1_63.
[CA72] Efficient Solution of Large Scale Lyapunov and Riccati Equations Arising in Model Order Reduction Problems
Jens Saak and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 8, No. 1, pp. 10085-10088, 2008.
DOI: 10.1002/pamm.200810085
[CA71] Projection-Based Model Reduction for LTV Descriptor System Using Multipoint Krylov-Subspace Projectors
Mohammad-Sahadet Hossain and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 8, No. 1, pp. 10081-10084, 2008.
DOI: 10.1002/pamm.200810081
[CA70] Flow Stabilisation by Dirichlet Boundary Control
René Schneider, Tobias Rothaug, and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 8, No. 1, pp. 10961-10962, 2008.
DOI: 10.1002/pamm.200810961
[CA69] Parametric Model Reduction with Sparse Grids
Ulrike Baur and Peter Benner
In B. Lohmann and A. Kugi (Eds.), Tagungsband GMA-FA 1.30 "Modellbildung, Identifizierung und Simulation in der Automatisierungstechnik", Workshop in Anif, 24.-26.9.2008, pp. 262-271, 2008. [ISBN: 978-3-9502451-3-4]
[CA68] Numerical Solution of Differential Riccati Equations Arising in Optimal Control for Parabolic PDEs
Hermann Mena and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 7, No. 1, pp. 2060063-2060064, 2007.
DOI: 10.1002/pamm.200700913
[CA67] A Robust Algorithm for Parametric Model Order Reduction
Lihong Feng and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 7, No. 1, pp. 1021501-1021502, 2007.
DOI: 10.1002/pamm.200700749
[CA66] Efficient Solution of Algebraic Bernoulli Equations Using H-Matrix Arithmetic
Ulrike Baur and Peter Benner
In K. Kunisch, G. Of, O. Steinbach (Eds.), Numerical Mathematics and Advanced Applications. Proceedings of ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications, Graz, Austria, September 2007, pp. 127-134, Springer-Verlag, Heidelberg, 2008. [ISBN: 978-3-540-69776-3]
DOI: 10.1007/978-3-540-69777-0_14
[CA65] Application of LQR Techniques to the Adaptive Control of Quasilinear Parabolic PDEs
Jens Saak and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 7, No. 1, pp. 2060013-2060014, 2007.
DOI: 10.1002/pamm.200700240
[CA64] Parallel Implementation of LQG Balanced Truncation for Large-Scale Systems
José M. Badía, Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, and Alfredo Remón
In I. Lirkov, S. Margenov, J. Waniewski (Eds.), Large-Scale Scientific Computing. 6th International Conference, LSSC 2007, Sozopol, Bulgaria, June 5-9, 2007, Revised Papers, Lecture Notes in Computer Science, Vol. 4818, pp. 227-234, Springer-Verlag, Berlin, Heidelberg, New York, 2008. [ISBN: 978-3-540-78825-6]
DOI: 10.1007/978-3-540-78827-0_24
[CA63] γ-Iteration for Descriptor Systems Using Structured Matrix Pencils
Peter Benner, Philip Losse, Volker Mehrmann, Lisa Poppe, and Timo Reis
In Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), Virginia Tech, Blacksburg, Virginia, USA, July 28-August 1, 2008 (CD Rom), 11 pages, 2008.
[CA62] Using the Superposition Property for Model Reduction of Linear Systems with a Large Number of Inputs
Peter Benner, Lihong Feng, and Evgenii B. Rudnyi
In Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems (MTNS2008), Virginia Tech, Blacksburg, Virginia, USA, July 28-August 1, 2008 (CD Rom), 12 pages, 2008.
[CA61] Experimental evaluation of new SLICOT solvers for linear matrix equations based on the matrix sign function
Vasile Sima and Peter Benner
In Proceedings of 2008 IEEE Multi-conference on Systems and Control. 9th IEEE International Symposium on Computer-Aided Control Systems Design (CACSD), Hilton Palacio del Rio Hotel, San Antonio, Texas, U.S.A., September 3-5, 2008, S. 601-606, Omnipress, Madison, WI, 2008. [ISBN: 978-1-4244-2223-4]
DOI: 10.1109/CACSD.2008.4627361
[CA60] Strategies for Parallelizing the Solution of Rational Matrix Equations
José M. Badía, Peter Benner, Maribel Castillo, Heike Faßbender, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In C. Bischof, M. Bücker, P. Gibbon, G.R. Joubert, T. Lippert, B. Mohr, and F. Peters (Eds.), Parallel Computing: Architectures, Algorithms and Applications. Proceedings of the International Conference ParCo 2007, NIC Series Volume 38, pp. 255-262, John von Neumann-Institut für Computing, Jülich, Germany, 2007. [ISBN: 978-3-9810843-4-4]
[CA59] Parametrische Modellreduktion durch impliziten Momentenabgleich (Parametric Model Reduction by Implicit Moment Matching) [German]
Lihong Feng and Peter Benner
In B. Lohmann and A. Kugi (Eds.), Tagungsband GMA-FA 1.30 "Modellbildung, Identifizierung und Simulation in der Automatisierungstechnik", Workshop in Anif, 26.-28.9.2007, pp. 34-47, 2007. [ISBN: 978-3-9502451-1-0]
[CA58] A Note on Projection Techniques for Model Order Reduction of Bilinear Systems
Lihong Feng and Peter Benner
In Theodore E. Simos, George Psihoyios, and Ch. Tsitouras (Eds.), Numerical Analysis and Applied Mathematics, International Conference of Numerical Analysis and Applied Mathematics. Corfu, September 16-21, 2007, AIP Conference Proceedings Vol. 936, pp. 208-211, Melville NY: AIP, 2007. [ISBN: 978-0-7354-0447-2]
DOI: 10.1063/1.2790110
[CA57] Fast System Identification and Model Reduction Solvers
Vasile Sima and Peter Benner
In B. R. Andrievsky and A.L. Fradkov (Eds.), Proceedings of the 9th IFAC Workshop "Adaptation and Learning in Control and Signal Processing" (ALCOSP 2007)}, August, 29-31, 2007, Saint Petersburg, Russia, IFAC-PapersOnline/Elsevier, 477-482, 2007.
DOI: 10.3182/20070829-3-RU-4911.00074
Retrieve local copy.
[CA56] MPC für nichtlineare partielle Differentialgleichungen parabolischen Typs (MPC for nonlinear partial differential equations of parabolic type) [German]
Peter Benner and Sabine Görner
In Tagungsband GMA-FA 1.40 "Theoretische Verfahren der Regelungstheorie" und GAMM-FA "Dynamik und Regelungstheorie", Workshops am Bostalsee, 24.-27.9.2006, pp. 91-101, 2006. [ISBN: 978-3-9810664-2-5]
[CA55] MPC for the Burgers Equation Based on an LQG Design
Peter Benner and Sabine Görner
Proceedings in Applied Mathematics and Mechanics, Vol. 6, No. 1, pp. 781-782, 2006.
DOI: 10.1002/pamm.200610371
[CA54]  Passivity Preserving Model Reduction via a Structured Lanczos Method
Peter Benner and Heike Faßbender
Proceedings of the 2006 IEEE Conference on Computer-Aided Control Systems Design, Munich, Germany, October 4-6, 2006, pp. 8-13, IEEE 2006. [ISBN: 0-7803-9797-5]
DOI: 10.1109/CACSD-CCA-ISIC.2006.4776616
[CA53]  A MATLAB Repository for Model Reduction Based on Spectral Projection
Peter Benner
Proceedings of the 2006 IEEE Conference on Computer-Aided Control Systems Design, Munich, Germany, October 4-6, 2006, pp. 19-24, IEEE 2006. [ISBN: 0-7803-9797-5]
DOI: 10.1109/CACSD-CCA-ISIC.2006.4776618
The corresponding software is (partially) available here.
[CA52] Parallel Solution of Large-Scale and Sparse Generalized Algebraic Riccati Equations
José M. Badía, Peter Benner, Rafael Mayo and Enrique S. Quintana-Ortí
In W. E. Nagel, W. V. Walter, and W. Lehner (Eds.), Euro-Par 2006 Parallel Processing: 12th International Euro-Par Conference, Lecture Notes in Computer Science, Vol. 4128, pp. 710-719. Springer-Verlag, Berlin, Heidelberg, New York, 2006.
DOI: 10.1007/11823285_74
[CA51]  A Numerical Algorithm for Robust Stabilization of Systems with Sector-Bounded Nonlinearity
Peter Benner
Preprints of the 5th IFAC Symposium on Robust Control Design, ROCOND'06, Toulouse, France, July 5-7, pp. 513-518, 2006.
DOI: 10.3182/20060705-3-FR-2907.00088
[CA50]  A SLICOT Implementation of a Modified Newton's Method for Algebraic Riccati Equations
Vasile Sima and Peter Benner
Proceedings of the 14th Mediterranean Conference on Control and Automation MED06, June 28-30, 2006, Ancona - Università Politecnica delle Marche, Italy (CD-ROM) (6 pages). [ISBN: 0-9786720-0-3]
DOI: 10.1109/MED.2006.328740
[CA49] Parallel Algorithms for Balanced Truncation of Large-Scale Unstable Systems
Sergio Barrachina, Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In Proceedings of 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005, pp. 2248-2253, 2005. [ISBN: 0-7803-9568-9]
DOI: 10.1109/CDC.2005.1582496
[CA48] New Hamiltonian Eigensolvers with Applications in Control
Peter Benner and Daniel Kressner
In Proceedings of 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005, pp. 6551-6556, 2005. [ISBN: 0-7803-9568-9]
DOI: 10.1109/CDC.2005.1583213
See also: Preprint #240, DFG Research Center MATHEON, Berlin, March 2005.
[CA47] Passivitätserhaltende Modellreduktion mit Balancierungstechniken (in German)
Peter Benner
In Tagungsband GMA-FA 1.30 "Modellbildung, Identifikation und Simulation in der Automatisierungstechnik", Workshop am Bostalsee, 28.-30.9.2005, pp. 152-168, 2005. [ISBN: 3-9810664-1-3]
[CA46] Parallel Order Reduction via Balanced Truncation for Optimal Cooling of Steel Profiles
José M. Badía, Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí Gregorio Quintana-Ortí, and Jens Saak
In J.C. Cunha, P.D. Mdeiros (Eds.), Euro-Par 2005 Parallel Processing: 11th International Euro-Par Conference, Lisbon, Portugal, August 30 - September 2, 2005, Lecture Notes in Computer Science, Vol. 3648, pp. 857-866, Springer-Verlag, Berlin, Heidelberg, New York, 2005.
DOI: 10.1007/11549468_93
See also: Preprint SFB393/05-02, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, January 2005.
[CA45] Parallel Solution of Large-Scale Algebraic Bernoulli Equations with the Matrix Sign Function Method
Sergio Barrachina, Peter Benner, and Enrique S. Quintana-Ortí
In T. Skeie, C.-S. Yang (Eds.), Proceedings of the 2005 International Conference on Parallel Processing Workshops, 14-17 June 2005, Oslo, Norway), pp. 189-193, IEEE Computer Society Press, 2005. [ISBN: 0-7695-2381-1]
DOI: 10.1109/ICPPW.2005.68
[CA44] A New Test for Passivity of Descriptor Systems
Peter Benner and Delin Chu
Oberwolfach Reports, Vol. 2, No. 1, pp. 571-574, 2005.
[CA43] Efficient numerical solution of the LQR-problem for the heat equation
Peter Benner and Jens Saak
Proceedings in Applied Mathematics and Mechanics, Vol. 4, No. 1, pp. 648-649, 2004.
DOI: 10.1002/pamm.200410305
[CA42] Parallel Algorithms for Balanced Truncation Model Reduction of Sparse Systems
José Manuel Badía, Peter Benner, Rafael Mayo, and Enrique S. Quintana-Ortí
In J. Dongarra, K. Madsen, J. Wasniewski (Eds.), Applied Parallel Computing: 7th International Conference, PARA 2004, Lyngby, Denmark, June 20-23, 2004. Revised Selected Papers, Lecture Notes in Computer Science, Springer-Verlag, Vol. 3732, pp. 267-275, 2006. [ISBN: 3-540-29067-4]
Original available from SpringerLink, DOI: 10.1007/11558958_32
[CA41] Factorized solution of the Lyapunov equation by using the hierarchical matrix arithmetic
Ulrike Baur and Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 4, No. 1, pp. 658-659, 2004.
DOI: 10.1002/pamm.200410310
[CA40] A Robust Numerical Method for Optimal H_inf Control
Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu
Proceedings 43rd IEEE Conference on Decision and Control CDC2004, pp. 424-425, Omnipress, Madison, WI, 2004. [ISBN: 0-7803-8683-3]
Very short version of [TR13].
[CA39] Computing Optimal Hankel Norm Approximations of Large-Scale Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Proceedings of 43rd IEEE Conference on Decision and Control CDC2004, pp. 3078-3083, Omnipress, Madison, WI, 2004. [ISBN: 0-7803-8683-3]
DOI: 10.1109/CDC.2004.1428939
The retrievable version is Preprint #116, DFG Research Center "Mathematics for Key Technologies", Berlin, April 2004.
[CA38] Computing Passive Reduced-Order Models for Circuit Simulation
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In Proceedings International Conference on Parallel Computing in Electrical Engeneering PARELEC 2004, pp. 146-151, IEEE Computer Society, Los Alamitos, CA, 2004. [ISBN: 0-7695-2080-4]
DOI: 10.1109/PCEE.2004.21
[CA37] Factorized Solution of Sylvester Equations with Applications in Control
Peter Benner
In B. De Moor, B. Motmans, J. Willems, P. Van Dooren, V. Blondel (Eds.), Proceedings Sixteenth International Symposium on: Mathematical Theory of Network and Systems, MTNS 2004, Leuven, Belgium, July 5-9, 2004.
[CA36] BDF Methods for Large-Scale Differential Riccati Equations
Peter Benner and Hermann Mena
In B. De Moor, B. Motmans, J. Willems, P. Van Dooren, V. Blondel (Eds.), Proceedings Sixteenth International Symposium on: Mathematical Theory of Network and Systems, MTNS 2004, Leuven, Belgium, July 5-9, 2004.
[CA35] Parallel Model Reduction of Large-Scale Linear Descriptor Systems via Balanced Truncation
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In M. Daydé, J.J. Dongarra, V. Hernández, J.M.L.M. Palma (Eds.), High Performance Computing for Computational Science - VECPAR 2004, Lecture Notes in Computer Science, No. 3402, pp. 340-353, Springer-Verlag, Berlin/Heidelberg 2005. [ISBN: 3-540-25424-2]
[CA34] A Structure-Preserving Method for Generalized Algebraic Riccati Equations Based on Pencil Arithmetic
Ralph Byers and Peter Benner
Proceedings of the European Control Conference ECC'03, September 1-4, 2003, Cambridge, UK. (CD Rom).
[CA33] Solving Linear Matrix Equations with SLICOT
Vasile Sima and Peter Benner
Proceedings of the European Control Conference ECC'03, September 1-4, 2003, Cambridge, UK. (CD Rom).
[CA32] Parallel Model Reduction of Large-Scale Unstable Systems
Peter Benner, Maribel Castillo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In G.R. Joubert, W.E. Nagel, F.J. Peters, W.V Walter (Eds.), Parallel computing: Software Technology, Algorithms, Architectures & Applications, Advances in Parallel Computing, Vol. 13, pp. 251-258, Elsevier B.V (North-Holland), 2004. [ISBN: 0-444-51689-1]
[CA31] Solving Algebraic Riccati Equations with SLICOT
Peter Benner and Vasile Sima
Proceedings of the 11th Mediterranean Conference on Control & Automation MED'03, June 18-20, 2003, Rhodes (CD Rom), paper IV01-1 (6 pages), 2003.
[CA30] A Service for Remote Model Reduction of Very Large Linear Systems
Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí and Gregorio Quintana-Ortí
In Proceedings of 17th International Parallel & Distributed Processing Symposium (IPDPS 2003), paper W16-PDSECA-22, 6 pages. IEEE Computer Society Press, 2003. [ISBN: 0-7695-1926-1]
DOI: 10.1109/IPDPS.2003.1213474
[CA29] Partial Stabilization of Generalized State-Space Systems Using the Disk Function Method
Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 2, No. 1, pp. 479-480, 2003.
DOI: 10.1002/pamm.200310222
[CA28] Solving Large Sparse Lyapunov Equations on Parallel Computers
José Manuel Badía, Peter Benner, Rafael Mayo, and Enrique S. Quintana-Ortí
In B. Monien, R. Feldmann (Eds.), Euro-Par 2002 Parallel Processing, Lecture Notes in Computer Science, No. 2400, pp. 687-690, Springer-Verlag, 2002. [ISBN: 3-540-44049-6]
DOI: 10.1007/3-540-45706-2_95
[CA27] A Sparse Approximate Inverse Preconditioner for the Method of Moments Accelerated with the Multilevel Fast Multipole Method
Peter Benner, Martin Brüning, Angelika Bunse-Gerstner, Rainer Bunger, Jan M. Reiter, and Jan Ritter
Proceedings of 2002 IEEE Intl. Symp. on Antennas & Propagation and USN/URSI Meeting, June 16-21, 2002, San Antonio, Texas, pp. 602-605.
DOI: 10.1109/APS.2002.1016157
[CA26] A Web Service for Model Reduction of Large-Scale Linear Systems on a Cluster
José Manuel Badía, Peter Benner, Maribel Castillo, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Proceedings of XIII Jornadas de Paralelismo, Lleida (Spain), pp. 383-388, 2002. [ISBN: 84-8409-159-7]
[CA25] Remote Parallel Model Reduction of Linear Time-Invariant Systems Made Easy
Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In J.M.L.M. Palma, V. Hernández, J.J. Dongarra, and A.A. Sousa (Eds.), High Performance Computing for Computational Science - VECPAR 2002, Lecture Notes in Computer Science, Springer-Verlag, No. 2565, pp. 255-268, 2003. [ISBN: 3-540-00852-7]
DOI: 10.1007/3-540-36569-9_16
Version in on-site conference proceedings:
A Mail Service for Parallel Model Reduction of Linear Time-Invariant Systems
Proceedings of VECPAR'02, 5th Intl. Meeting on High-Performance Computing for Computational Science, Porto, Portugal, June 26-28, 2002, pp. 735-746.
[CA24] Enhanced Services for Remote Model Reduction of Large-Scale Dense Linear Systems
Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In J. Fagerholm, J. Haataja, J. Järvinen, M. Lyly, P. Raback, and V. Savolainen (Eds.), Applied Parallel Computing. PARA'02 6th International Conference, Espoo (Finland), 2002, Lecture Notes in Computer Science, No. 2367, pp. 329-338, Springer-Verlag, 2002. [ISBN: 3-540-43786-X]
DOI: 10.1007/3-540-48051-X_33
[CA23] A Coarse-Grain Parallel Solver for Riccati Equations
Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, and Vicente Hernández
In G.R. Joubert, A. Murli, F.J. Peters, M. Vanesschi (Eds.), Parallel Computing. Advances and Current Issues. Proceedings of the International Conference ParCo2001, pp. 274-281, Imperial College Press, London, UK, 2002. [ISBN: 1-86094-315-2]
[CA22] Efficient Algorithms for Large-Scale Quadratic Matrix Equations
Peter Benner
Proceedings in Applied Mathematics and Mechanics, Vol. 1, No. 1, pp. 492-495, 2002.
[CA21] Computing Roots of Matrix Products
Peter Benner and Heike Faßbender
Zeitschrift für angewandte Mathematik und Mechanik, Vol. 81, Suppl. 3, pp. S717-S718, 2001.
[CA20] On a Numerical Method for the Regularization of Descriptor Systems
Peter Benner
Zeitschrift für angewandte Mathematik und Mechanik, Vol. 81, Suppl. 3, pp. S707-S708, 2001.
[CA19] Partial Stabilization of Large-Scale Discrete-Time Linear Control Systems
Peter Benner, Maribel Castillo, and Enrique S. Quintana-Ortí
Proceedings of the 2001 ICPP Workshops (Workshop on High Performance Scientific and Engineering Computing with Applications), Valencia, September 3-7, 2001, pp. 93-98, IEEE Computer Society Press, Los Alamitos, CA, 2001. [ISBN: 0-7695-1260-7]
DOI: 10.1109/ICPPW.2001.951856
[CA18] PSLICOT Routines for Model Reduction of Stable Large-Scale Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Proceedings of the Third NICONET Workshop on Numerical Software in Control Engineering, Louvain-la-Neuve, Belgium, January 19, 2001, pp. 39-44.
[CA17] Model Reduction of Large-Scale Dense Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Proceedings of the IEE UKACC International Conference CONTROL 2000, Cambridge, UK, 4-7 September 2000, IEE ZZ057 (CD Rom), 2000. [ISBN: 0-85296-240-1]
[CA16] Singular Perturbation Approximation of Large, Dense Linear Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
Proceedings of the 2000 IEEE International Symposium on Computer Aided Control System Design, Anchorage, Alaska, USA, September 25-27, 2000, pp. 255-260. Omnipress, Madison, WI, 2000.
DOI: 10.1109/CACSD.2000.900220
[CA15] Solving Discrete-Time Periodic Riccati Equations on a Cluster
Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí and Vicente Hernández
In A. Bode, T. Ludwig, W. Karl, and R. Wismüller (Eds.), Euro-Par 2000 Parallel Processing, Lecture Notes in Computer Science, No. 1900, pp. 824-828, Springer-Verlag, 2000. [ISBN: 3-540-67956-1]
DOI: 10.1007/3-540-44520-X_113
[CA14] Efficient Numerical Model Reduction Methods for Discrete-Time Systems
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In I. Troch, F. Breitenecker (Eds.), Proceedings of the IMACS Symposium on Mathematical Modelling, 3rd MATHMOD Vienna, Vienna University of Technology, Austria, February 2-4, 2000, Vol. 1, pp. 277-280, ARGESIM Reports No. 15. [ISBN: 3-901608-15-X]
[CA13] Arithmetic for Rectangular Matrix Pencils
Peter Benner and Ralph Byers
In O. Gonzalez (editor), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast-Island of Hawaii, Hawaii, USA, August 22-27, 1999, pp. 75-80. [ISBN: 0-7803-5449-4]
DOI: 10.1109/CACSD.1999.808627
[CA12] Numerical Solution of Linear-Quadratic Control Problems for Descriptor Systems
Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu
In O. Gonzalez (editor), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast-Island of Hawaii, Hawaii, USA, August 22-27, 1999, pp. 46-51. [ISBN: 0-7803-5449-4]
DOI: 10.1109/CACSD.1999.808622
[CA11] Solving Linear and Quadratic Matrix Equations on Distributed Memory Parallel Computers
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In O. Gonzalez (editor), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast-Island of Hawaii, Hawaii, USA, August 22-27, 1999, pp. 64-69. [ISBN: 0-7803-5449-4]
DOI: 10.1109/CACSD.1999.808625
[CA10] Initializing Newton's Method for Discrete-Time Algebraic Riccati Equations Using the Butterfly SZ Algorithm
Peter Benner and Heike Faßbender
In O. Gonzalez (editor), Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast-Island of Hawaii, Hawaii, USA, August 22-27, 1999, pp. 70-74. [ISBN: 0-7803-5449-4]
DOI: 10.1109/CACSD.1999.808626
[CA9] Solving Stable Stein Equations on Distributed Memory Computers
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
In P. Amestoy, P. Berger, M. Daydé, I. Duff, V. Frayssé, L. Giraud and D. Ruiz (Eds.), EuroPar'99 Parallel Processing, Lecture Notes in Computer Science, No. 1685, Springer-Verlag, 1999, pp. 1120-1123. [ISBN 3-540-66443-2]
DOI: 10.1007/3-540-48311-X_156
[CA8] Accelerating Newton's Method for Discrete-Time Algebraic Riccati Equations
Peter Benner
In A. Beghi, L. Finesso, and G. Picci (Eds.), Mathematical Theory of Networks and Systems. Proceedings of the MTNS-98 Symposium held in Padova, Italy, July, 1998, pp. 569-572, Il Poligrafo, Padova, 1998. [ISBN: 88-7115-117-8]
[CA7] An Arithmetic for Matrix Pencils
Peter Benner and Ralph Byers
In A. Beghi, L. Finesso, and G. Picci (Eds.), Mathematical Theory of Networks and Systems. Proceedings of the MTNS-98 Symposium held in Padova, Italy, July, 1998, pp. 573-576, Il Poligrafo, Padova, 1998. [ISBN: 88-7115-117-8]
[CA6] Improving the efficiency and accuracy of the MATLAB Control Toolbox using SLICOT-based gateways
Vasile Sima, Peter Benner, Sabine Van Huffel, and Andras Varga
In A. Beghi, L. Finesso, and G. Picci (Eds.), Mathematical Theory of Networks and Systems. Proceedings of the MTNS-98 Symposium held in Padova, Italy, July, 1998, pp. 673-676, Il Poligrafo, Padova, 1998. [ISBN: 88-7115-117-8]
[CA5] Efficient Solution of Coupled Lyapunov Equations via Matrix Sign Function Iteration.
Peter Benner, José M. Claver, and Enrique S. Quintana-Ortí
Proceedings of the 3rd Portuguese Conference on Automatic Control CONTROLO'98, Coimbra, September 9-11, 1998, pp. 205-210.
[CA4] Numerical Solution of Special Algebraic Riccati Equations via an Exact Line Search Method
Peter Benner
Proceedings of the European Control Conference ECC97 (CD-ROM), Paper 786, BELWARE Information Technology, Waterloo (B), 1997.
[CA3] A New Method for the Hamiltonian Eigenvalue Problem
Peter Benner, Volker Mehrmann, and Hongguo Xu
Proceedings of the European Control Conference ECC97(CD-ROM), Paper 785, BELWARE Information Technology, Waterloo (B), 1997.
[CA2] Disk Functions and their Relationship to the Matrix Sign Function
Peter Benner and Ralph Byers
Proceedings of the European Control Conference ECC97 (CD-ROM), Paper 936, BELWARE Information Technology, Waterloo (B), 1997.
[CA1] Step Size Control for Newton's Method Applied to Algebraic Riccati Equations
Peter Benner and Ralph Byers
Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, pp. 177-181, SIAM, Philadelphia, 1994.

Technical reports

NOTE: The technical reports listed below either represent papers that will not be published elsewhere or longer versions of published articles (e.g., containing more algorithmic details or numerical examples).

[TR30]  [new] MORLAB-3.0 - Model Order Reduction Laboratory
Peter Benner, Steffen W. R. Werner
DOI: 10.5281/zenodo.842659
September 2017
[TR29] Balanced Truncation of Linear Time-Invariant Systems at a Single Frequency
Xin Du, Peter Benner, Guanghong Yang, and Dan Ye
MPI Magdeburg Preprint MPIMD/13-02, January 2013.
[TR28] H2-Optimality Conditions for Structured Dynamical Systems
Christopher Beattie and Peter Benner
MPI Magdeburg Preprint MPIMD/14-18, October 2014.
[TR27] Computational Solutions of a Family of Generalized Procrustes Problems
Jens Fankhänel and Peter Benner
Preprintreihe der Fakultät für Mathematik, Preprint 14-06, TU Chemnitz, June 2014.
[TR26] Numerical Solution of Eigenvalue Problems for Alterating Matrix Polynomials and Their Application in Control Problems for Descriptor Systems
Peter Benner, Philip Losse, Volker Mehrmann, and Matthias Voigt
MPI Magdeburg Preprint MPIMD/13-24, December 2013.
[TR25] FORTRAN 77 Subroutines for the Solution of Skew-Hamiltonian/Hamiltonian Eigenproblems - Part II: Implementation and Numerical Results
Peter Benner, Matthias Voigt, and Vasile Sima
SLICOT Working Note 2013-2, August 2013.
[TR24] FORTRAN 77 Subroutines for the Solution of Skew-Hamiltonian/Hamiltonian Eigenproblems - Part I: Algorithms and Applications
Peter Benner, Matthias Voigt, and Vasile Sima
SLICOT Working Note 2013-1, August 2013.
[TR23] Sparse-Dense Sylvester Equations in H2-Model Order Reduction
Peter Benner, Martin Köhler, and Jens Saak
MPI Magdeburg Preprint MPIMD/11-11, December 2011.
[TR22] Model Predictive Control Based on an LQG Design for Time-Varying Linearizations
Peter Benner and Sabine Hein
Chemnitz Scientific Computing Preprints 09-07, TU Chemnitz, November 2009/March 2010.
[TR21] A Galerkin-Newton-ADI Method for Solving Large-Scale Algebraic Riccati Equations
Peter Benner and Jens Saak
Preprint SPP1253-090, DFG Priority Programme 1253 Optimization with Partial Differential Equations, January 2010.
[TR20] Projection-Based Model Reduction for Time-Varying Descriptor Systems: New Results
Mohammad-Sahadet Hossain and Peter Benner
MPI Magdeburg Preprint MPIMD/12-04, February 2012.
[TR19] The SLICOT Toolboxes - a Survey
Peter Benner, Daniel Kressner, Vasile Sima, and Andras Varga
SLICOT Working Note 2009-1, August 2009.
[TR18] Modellordnungsreduktion für strukturmechanische FEM-Modelle von Werkzeugmaschinen [German]
Peter Benner
Project Report, Chemnitz University of Technology, May 2008.
[TR17] Balanced Truncation Model Reduction of Large and Sparse Generalized Linear Systems
José M. Badía, Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, and Alfredo Remón
Chemnitz Scientific Computing Preprints 06-04, TU Chemnitz, November 2006.
[TR16] Solving Large-Scale Generalized Algebraic Bernoulli Equations via the Matrix Sign Function
Sergio Barrachina, Peter Benner and Enrique S. Quintana-Ortí
Preprint SFB393/05-15, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, December 2005.
[TR15] Linear-Quadratic Regulator Design for Optimal Cooling of Steel Profiles
Peter Benner and Jens Saak
Preprint SFB393/05-05, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, April 2005.
[TR14] Robust Numerical Methods for Robust Control
Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu
Preprint 06-2004, Institut für Mathematik, TU Berlin, February 2004.
[TR13] Experimental Evaluation of the Parallel Model Reduction Routines in PSLICOT
Peter Benner, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí
SLICOT Working Note 2002-7, August 2002.
[TR12] Model Reduction Based on Iterative Solvers for Computing the System Gramians
Peter Benner
NICONET Newsletter, Vol. 8, pp. 5-7, 2002.
[TR11] Schnelle Löser zur Berechnung elektromagnetischer Felder (in German)
Peter Benner, Martin Brüning, and Angelika Bunse-Gerstner
Project report, Zentrum für Technomathematik, Universität Bremen and EADS Bremen, March 2001.
[TR10] Numerical Computation of Deflating Subspaces of Embedded Hamiltonian Pencils
Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu
Preprint SFB393/99-15, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, June 1999.
[TR9] A Unified Deflating Subspace Approach for Classes of Polynomial and Rational Matrix Equations
Peter Benner, Ralph Byers, Volker Mehrmann, and Hongguo Xu
Preprint SFB393/00-05, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz, January 2000.
[TR8] DAREX - A Collection of Benchmark Examples for Discrete-Time Algebraic Riccati Equations (Version 2.0)
Jörn Abels and Peter Benner
SLICOT Working Note 1999-16, December 1999.
This report updates [TR2]
[TR7] CAREX - A Collection of Benchmark Examples for Continuous-Time Algebraic Riccati Equations (Version 2.0)
Jörn Abels and Peter Benner
SLICOT Working Note 1999-14, November 1999.
This report updates [TR1]
[TR6] SLICOT Drives Tractors!
Peter Benner and Heike Faßbender
NICONET Newsletter, Vol. 2, pp. 17-22, 1999.
See also: NICONET Report 1999-2, Working Group on Software, February 1999.
[TR5] HAMEV and SQRED: Fortran 77 Subroutines for Computing the Eigenvalues of Hamiltonian Matrices Using Van Loans's Square Reduced Method
Peter Benner, Ralph Byers, and Eric Barth
Preprint SFB393/96-06, Sonderforschungsbereich 393 - Numerische Simulation auf massiv parallelen Rechnern, TU Chemnitz-Zwickau, May 1996.
[TR4] A Restarted Symplectic Lanczos Method for the Hamiltonian Eigenvalue Problem
Peter Benner and Heike Faßbender
Technical Report SPC 95_28, TU Chemnitz-Zwickau, October 1995, Errata.
[TR3] Newton's Method with Exact Line Search for Solving the Algebraic Riccati Equation
Peter Benner and Ralph Byers
Technical Report SPC 95_24, TU Chemnitz-Zwickau, October 1995.
[TR2] A Collection of Benchmark Examples for the Numerical Solution of Algebraic Riccati Equations II: Discrete-Time Case
Peter Benner, Alan J. Laub, and Volker Mehrmann
Technical Report SPC 95_23, TU Chemnitz-Zwickau, Dezember 1995, Errata.
[TR1] A Collection of Benchmark Examples for the Numerical Solution of Algebraic Riccati Equations I: Continuous-Time Case
Peter Benner, Alan J. Laub, and Volker Mehrmann
Technical Report SPC 95_22, TU Chemnitz-Zwickau, October 1995.

Lecture notes

[L3] Advanced Computational Methods for CACSD
Peter Benner and Paul Van Dooren
Tutorial workshop held at European Control Conference 2003, Cambridge, UK, September 1-4, 2003.
Revised version June 22, 2004.
[L2] Numerik für Ingenieure und Naturwissenschaftler (in German)
Angelika Bunse-Gerstner, Peter Benner, and Heike Faßbender
Zentrum für Technomathematik, Universität Bremen, Oktober 2000.
[L1] Mathematik in der Berufspraxis (in German)
Peter Benner (editor), Berichte aus der Technomathematik, Report 99-05, August 1999.
Collection of protocols from a lecture series given by mathematicians from industry during the summer term 1998.

Theses

[T2] Contributions to the Numerical Solution of Algebraic Riccati Equations and Related Eigenvalue Problems
Peter Benner
Dissertation, Fakultät für Mathematik, TU Chemnitz-Zwickau, 1997.
Published by Logos-Verlag, Berlin, June 1997 [ISBN: 3-931216-70-5].
Summary (in German).
[T1] Ein orthogonal symplektischer Multishift Algorithms zur Lösung der algebraischen Riccatigleichung (in German)
Peter Benner
Diplomarbeit (Master's Thesis), Institut für Geometrie und Praktische Mathematik, RWTH Aachen, March 1993.

Other publications

[OP18] Drogen, Herbizide und numerische Simulation
Peter Benner, Hermann Mena, and René Schneider
Mitteilungen der Deutschen Mathematiker-Vereinigung, Vol. 23, No. 4, pp. 222–225, 2015.
Translated to German from [OP12].
[OP17] Nanoelectronic COupled Problems Solutions - nanoCOPS
E. Jan W. ter Maten, Piotr Putek, Michael Günther, Caren Tischendorf, Christian Strohm, Wim Schoenmaker, Peter Meuris, Bart De Smedt, Peter Benner, et al.
Preprint BUW-IMACM 15/36, Bergische Universität Wuppertal, Germany, 2015.
[OP16] The NanoCOPS Project on Algorithms for Nanoelectronic Coupled Problems Solutions
R. Janssen, J. ter Maten, C. Tischendorf, H.-G. Brachtendorf, K. Bittner, W. Schoenmaker, P. Benner, L. Feng, R. Pulch, F. Deleu, and A. Wieers
In B. Schrefler, E. Oñate, and M. Papadrakakis (Eds.), VI International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED Problems 2015, Venice, Italy, pp. 1029-1036, 2015.
[OP15] nanoCOPS: Nanoelectronic COupled Problem Solutions
P. Benner, K. Bittner, H.-G. Brachtendorf, H. De Gersen, F. Deleu, L. Feng, T. Götthans, M. Günther, R. Janssen, T. Kratochvíl,
Q. Liu, P. Meuris, R. Pulch, P- Putek, P. Reynier, S. Schöps, J. Schneider, W. Schoenmaker, C. Strohm, E. Jan W. ter Maten, C. Tischendorf, and A. Wieers
ECMI Newsletter, Vol. 56, pp. 62-67, 2014.
[OP14] nanoCOPS: Parametric Modeling and Model Order Reduction of Coupled Problems
Peter Benner, Lihong Feng, Peter Meuris, and Wim Schoenmaker
ECMI Newsletter, Vol. 56, pp. 68-69, 2014.
[OP13] Das Max-Planck-Institut für Dynamik komplexer technischer Systeme
Peter Benner, Gabriele Ebel, Victoria Grimm, and Andreas Seidel-Morgenstern
In G. Ihlow, H. Just, Ch. Kretzschmann, M. Maas, L. Modes, A. Neubauer, K. Pusch, H.-J. Rasehorn, R. Schmidt, J. Schulz, and J. Weschke (Eds.), Der Maschinen- und Anlagenbau in der Region Magdeburg zu Beginn des 21. Jahrhunderts, pp. 590-594, Verlag Delta-D, Magdeburg, 2014. [ISBN: 978-3-935831-51-2]
[OP12] Drugs, Herbicides, and Numerical Simulation
Peter Benner, Hermann Mena, and René Schneider
Snapshots of Modern Mathematics from Oberwolfach, No. 10/2014, 9 pages, September 2014.
[OP11] Compact Models for Simulation, Control and Optimization of Complex Dynamical Systems
Peter Benner
Yearbook 2011/12 of the Max Planck Society, May 2012.
[OP10] Modeling and Optimal Control of Chemical Mechanical Planarization
Susan Dürigen, Peter Benner, Uwe Stöckgen, and Jens Heinrich
In T. Lery, M. Primicerio, M.J. Esteban, M. Fontes, Y. Maday, V. Mehrmann, G. Quadros, W. Schilders, A. Schuppert, and H. Tewkesbury (Eds.), European Success Stories in Industrial Mathematics, p. 76, Springer-Verlag, Berlin/Heidelberg, 2011. [ISBN: 978-3-642-23847-5]
[OP9] O-MOORE-NICE! New methodologies and algorithms for design and simulation of analog integrated circuits
Joost Rommes, Davit Harutyunyan, Michael Striebel, Luciano De Tommasi, Jan ter Maten, Peter Benner, Tom Dhaene, Wil Schilders, and Marcel Sevat
ECMI Newsletter, Vol. 47, pp. 17-20, 2010.
[OP8] The GAMM Activity Group Applied and Numerical Linear Algebra
Peter Benner and Daniel Kressner
IMAGE (Bulletin of the ILAS), Vol. 43, pp. 25-26, 2009.
[OP7] System Reduction for Nanoscale IC Design (SyreNe)
Peter Benner
ECMI Newsletter, Vol. 45, pp. 18-21, 2009.
[OP6] Model Reduction at ICIAM '07
Peter Benner
SIAM News, Vol. 40, No. 8, pp. 16-17, October 2007.
[OP5] Model Reduction using Center and Inertial Manifolds
Peter Benner
Berlin-Braunschweig-Chemnitz Workshop Recent Advances in Model Reduction, TU Chemnitz, 27 November 2006.
[OP4] NICONET participation in the 7th European Control Conference, ECC03, University of Cambridge, UK, September 1-4, 2003
Peter Benner
NICONET Newsletter, Vol. 11, pp. 5-8, 2003.
[OP3] The freeware numerical subroutine library SLICOT for systems and control theory
Ad van den Boom, Vasile Sima, Peter Benner, and Sabine Van Huffel
Abstracts 17-th Benelux Meeting on Systems and Control, Mierlo, The Netherlands, March 1998.
(!WinWord document!)
[OP2] NICONET - Ein europäisches Netzwerk zur Numerik in der Kontrolltheorie (in German)
Peter Benner
Kopien der Vortragsfolien, Gemeinsamer Workshop GAMM-Fachausschuß "Dynamik und Regelungstheorie" und VDI/VDE-GMA Ausschuß 1.4 "Theoretische Verfahren der Regelungstechnik", Kassel, March 2-3, 1998, pp. 185-193.
[OP1] Collections of Benchmark Examples in Control
Peter Benner and Volker Mehrmann
WGS Newsletter, Vol. 10, pp. 7-8, 1996.
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Peter Benner, benner@mpi-magdeburg.mpg.de