A shift parameter generation technique for the low-rank ADI iteration for large Lyapunov equations is discussed, which is based on a residual minimization principle.

In this survey article, Peter Benner, Zvonimir Bujanović (Uni Zagreb), Patrick Kürschner and Jens Saak present a extensive comparison of low-rank solvers for large-scale algebraic Riccati equations.

Melina Freitag (Uni Bath) and Patrick Kürschner investigate the effect of inexact linear solves in rational Krylov subspace and low-rank ADI methods for large matrix equations. Dynamic stopping criteria are developed that decrease the amount of work spent in solving the sequences of linear systems.

Patrick Kürschner, Sergey Dolgov (Uni Bath), Kameron Decker Harris (Uni Washington), and Peter Benner investigate a matrix regression problem arising in computational neuroscience. The problem is formulated as large-scale algebraic matrix equation which is solved by a greedy low-rank algorithm.

Die SIAM Conference on Applied Linear Algebra (SIAM-ALA18) takes place on 4-8 May 2018 at the Hong Kong Baptist University. The CSC members Carolin Penke, Davide Palitta, and Patrick Kürschner participate with talks.

Patrick Kürschner is getting funded by EU-MORNET for a six week "short-term-scientific-mission" to Bath, UK. The purpose of this research visit is to investigate together with Melina Freitag the effects of inexact linear solves in low-rank solvers for large-scale matrix equations.

Martin Redmann (WIAS Berlin) and Patrick Kürschner propose error bounds for model reduction via time-limited balanced truncation.

Patrick Kürschner is organizing a minisymposium on "Matrix equations: theory, numerics and applications" at the International Conference on Scientific Computation and Differential Equations (SciCADE) in Bath, UK. Newest group member Tony Stillfjord will also attend this minisymposium with a talk.

Patrick Kürschner investigates model reduction via a time-restricted balanced truncation framework. A rational Krylov subspace method is considered for dealing with the arising large scale matrix functions and equations. The numerical experiments reveal an improved accuracy in the time region of interest compared to ordinary balanced truncation.

In this work, Christian Kuehn and Patrick Kürschner study the numerical approximation of local fluctuations of certain classes SPDEs. Combined ERror EStimates (CERES) are developed for the four main errors: the spatial discretization error, the local linearization error, the local relaxation error to steady state, and the approximation error w.r.t. the covariance matrix computed by an iterative low-rank algorithm for Lyapunov equations.

Melina Freitag, Patrick Kürschner and Jennifer Pestana present some new bounds for the convergence of preconditioned GMRES when applied to solve the linear systems arising in methods for large-scale, nonsymmetric eigenvalue problems.

The 16th GAMM Workshop Applied and Numerical Linear Algebra took place at the Hamburg UT. Peter Benner, Jens Saak, Nicodemus Banagaaya, Patrick Kürschner and Martin Stoll from the CSC / NDS group attended. Martin Stoll, Jens Saak and Patrick Kürschner presented recent result in contributed talks.

Akwum Onwunta and Patrick Kürschner present minisymposium talks at the CMAM-7 in Jyväskylä;, Finland. Martin Stoll is coorganizing a minisymposium with Boris Khoromskij (MPI Leipzig).

CSC and NDS contributed several talks (Peter Benner, Jens Saak, Patrick Kürschner, Akwum Onwunta, Martin Soll, Christian Himpe, Xin Liang) to minisymposia at this year's ILAS Conference with 440 participants at KU Leuven. Furthermore, Peter Benner co-organized the invited minisymposium "Matrix Equations" jointly with Beatrice Meini (U Pisa).

Peter Benner, Zvonimir, Bujanovic, Patrick Kürschner and Jens Saak present a quadratic version of the ADI iteration for directly handling large-scale algebraic Riccati equations.

The fifth workshop on matrix equations and tensor techniques is held in Bologna, Italy from September 21-22, 2015. It is coorganized by the CSC group. Sergey Dolgov is a keynote speaker and Jens Saak, Heiko Weichelt, Patrick Kürschner will give contributed talks.

The CSC research group organizes the annual GAMM ANLA workshop which takes place at the Max Planck Institute Magdeburg from 9.-10. July 2015

Peter Benner, Patrick Kürschner und Jens Saak present in this work computational approaches for an numerically efficient execution of frequency-limited balanced trunction for large-scale systems.

The CSC research group is looking for a student / research assistant to continue the work on the double and triple pendulum.

The SIAM Student Chapter at TU Delft is organizing the Student Krylov Day 2015. As representatives of the SIAM Student Chapter Magdeburg, Heiko Weichelt and Patrick Kürschner will give contributed talks.

Peter Benner, Patrick Kürschner and Jens Saak discuss a numerical algorithm for solving large-scale, nonsymmetric algebraic Ricatti equations, which combines a Newton's method with the low-rank ADI iteration for Sylvester equations.

Peter Benner, Jonas Denißen, Patrick Kürschner and Jens Saak attend the workshop within the DAAD project Optimal Damping of Vibrating Systems in Osijek (Croatia). The workshop is supported by the German Academic Exchange Service (DAAD), Zeidler-Forschungs-Stiftung and the department of mathematics, J. J. Strossmayer University of Osijek.

Peter Benner, Patrick Kürschner, Zoran Tomljanović, and Ninoslav Truhar present an approach to compute the optimal gain which minimizes the impulse response energy of a vibrational system. The used method employs the parametric dominant pole algorithm to produce reduced order models in order to decrease the computational cost of the optimization procedure.

Patrick Kürschner and Jens Saak presented their respective latest results on the efficient computation of frequency limited Gramain matrices and inexact Newton based solution of the LQR problem for linearized flow problems at the joint meeting of the GAMM ANLA and its spanish counterpart ALAMA that took place in Barcelona July 14-16. Peter Benner acted as part of the organizing commitee.

The Householder Symposium XIX on numerical linear algebra took place in Spa (Belgium) from 06/08 - 06/13. The CSC group was represented by talks of Peter Benner, Martin Stoll and Patrick Kürschner as well as by a poster of Matthias Voigt.

The 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics is taking place in Erlangen, Germany. Patrick Kürschner, Jens Saak, Jonas Denißen, Norman Lang, Akwum Onwunta, Björn Baran, Ulrike Baur, Zvonimir Bujanovic, Jan Heiland, Martin Köhler, Matthias Voigt, and Sara Grundel will give talks in the contributed sections.

At the 9. Elgersburg Workshop M. Voigt and P. Kürschner represent the Computational Methods in Systems and Control Theory group by two talks.

The recent issue of SIAM News (Januar 2014) reports about the opening workshop of the SIAM Student Chapter Magdeburg. The workshop took place at the MPI Magdeburg on June 19th 2013. Edda Klipp from the Humboldt University Berlin was invited as the main speaker.

The Zeidler-Forschungs-Stiftung supports the project "Optimal damping of vibrating systems" by a 50.000 Euro grant. Project partner of the Max Planck Institute is the J. J. Strossmayer University in Osijek (Croatia).

The Computational Methods in Systems and Control Theory group is proud to welcome a number of new group members. Jan Heiland and Xin Du are starting as new Post Docs, Christian Miller switches status to a research assistant and Carolin Penke and Steffen Hermann take up their work as student assistants of the group.

Peter Benner, Patrick Kürschner, and Matthias Voigt participate as invited guests in the Oberwolfach Workshop: Numerical Solution of PDE Eigenvalue Problems (11/17 - 11/23/13). Patrick Kürschner and Matthias Voigt are supported as Oberwolfach Leibniz Graduate Students (OWLG).

The authors present novel shift strategies for low-rank ADI methods for the numerical solution of large-scale Lyapunov and Sylvester equations. In the proposed approaches shift parameters are computed automatically during the ADI iteration. Numerical test show that these new shifts outperform existing strategies in several cases, especially for problems with complex spectra.

The GAMM Workshop Applied and Numerical Linear Algebra will take place at the Bergische Universität Wuppertal from 09/09 - 09/10/2013. Peter Benner, Matthias Voigt, Jens Saak, Jessica Bosch und Patrick Kürschner are participants and in part give contributed talks.

The Numerical Analysis and Scientific Computation with Applications (NASCA13) conference will take place in Calais, France from 06/24 - 06/26/2013. Peter Benner gives an invited and Patrick Kürschner a contributed presentation.

Peter Benner will co-organize (with Albert Cohen, Mario Ohlberger, Karen Willcox) the CIRM workshop Model Reduction and Approximation for Complex Systems, June 10-14, 2013, CIRM Luminy, France. Ulrike Baur, Patrick Kürschner, Tobias Breiten, Lihong Feng and Sara Grundel from the CSC group will also participate.

Studies on the low-rank ADI for large-scale Stein equations
Contact: Patrick Kürschner

Deepak Matcha Venkat from IIT Bombay starts as anintern and will investigate the two-degree of freedom control of the double and triple pendulum.

Peter Benner and Patrick Kürschner present new results and numerical enhancements for the low-rank ADI iteration for large-scale Sylvester matrix equations.

Melina Freitag (University of Bath) and Patrick Kürschner present new results regarding convergence and preconditioning of inexact two-sided eigenvalue iterations. A novel equivalence results between those methods and a simplified two-sided Jacobi-Davidson is also established.

Christian Miller from the FH Kempten starts as student research assistant and diploma candidate. He will investigate the swing-up of the double and triple pendulum via feedforward control. The obtained results will be validated on a real pendulum experiment.

The 84th Annual Meeting of the International Association of Applied Mathematics and Mechanics is taking place in Novi Sad, Serbia. Peter Benner, Tobias Breiten, Patrick Kürschner, Jessica Bosch, Jens Saak, Martin Redmann, Jonas Denißen and Norman Lang will give talks in the contributed sections.

Zoran Tomljanović from the J. J. Strossmayer University of Osijek, Department of Mathematics, Osijek, Croatia visits CSC in the period February 5 - 20, 2013. The purpose of his stay is to work with Peter Benner, Jonas Denißen, Patrick Kürschner and Matthias Voigt on the newly approved DAAD project "Optimal damping of vibrating systems".

The DAAD (German Academic Echange Service) exchange project project "Optimal damping of vibrating systems" with Croatia for 2013-2014 has been approved. Projectmembers are Ninoslav Truhar, Zoran Tomljanović, Peter Benner, Jonas Denißen, Patrick Kürschner and Matthias Voigt.

A CG-Method with ADI preconditioning for the solution of large sparse Lyapunov equations with symmetric coefficient matrices
Contact: Jens Saak

We consider balanced truncation model order reduction for symmetric second order systems. The occurring large-scale generalized and structured Lyapunov equations are solved with a specially adapted low-rank ADI type method. Stopping criteria for this iteration are investigated and a new result concerning the Lyapunov residual within the low-rank ADI method is established. We also propose a goal oriented stopping criterion which tries to incorporate the balanced truncation approach already during the ADI iteration. The model reduction approach using the ADI method with different stopping criteria is evaluated on several test systems.

Swing up and stabilization of the inverse double- and triplependulum. Contact: Patrick Kürschner. This news entry is expired.

This years second meeting of the GAMM activity group on "Dynamics and Control" will take place together with the GMA activity groups 1.30 and 1.40 as usual on a bi-anual basis. The meeting is scheduled September 17 to 21 at Sporthotel Anif near Salzburg. The talks of the GAMM activity group will take place on Wednesday 19th and contain contributions by Patrick Kürschner, Jens Saak and M. Monir Uddin. Also Matthias Voigt is participating as member of the activity group.

Patrick Kürschner will present some of his research results at the 3rd IMA Conference on Numerical Linear Algebra and Optimisation which takes place in Birminham, UK, from 10th until 12th of September 2012.

From June 18th to 22nd the SIAM Applied Linear Algebra conference 2012 is taking place in Valencia (Spain). The Computational Methods in Systems and Control Theory group is organizing two Minisymposia (Jens Saak and Martin Stoll) there. Moreover the group presents five invited Minisymposium talks (Peter Benner, Kapil Ahuja, Tobias Breiten, Jens Saak and Martin Stoll), as well as three contributed talks (Martin Hess, Patrick Kürschner und M. Sahadet Hossain) in several sections.

Also this year our group contributes to the GAMM Annual Meeting. Martin Stoll and Matthias Voigt participate in organizing two Minisymposia. The both and Tobias Breiten, Sara Grundel, Martin Heß, Patrick Kürschner, Thomas Mach, and Jens Saak give talks at the GAMM Annual Meeting 2012 in Darmstadt.

This paper presents the results obtained within the FVV pilot study concerning model order reduction for EMBS.

Numerical solution of low-rank representations of band-limited Gramians
In this thesis we investigate the representation of band-limited Gramians by matrix equations and the low-rank approximation of thereof.
Contact: Patrick Kürschner

Simultaneous iterative solution of the adjoint linear systems in the dual low-rank ADI iteration for Lyapunov equations
Solving dual large-scale Lyapunov equations is a main step for carrying out balanced truncation model order reduction for linear, time-invariant control systems. Both Lyapunov equation can be solved simultaneously in one run of the dual low-rank ADI iteration. Here we are going to investigate the simultaneous iterative solution of the occurring adjoint linear systems with BiCG / QMR.
Contact: Patrick Kürschner

Peter Benner, Patrick Kürschner and Jens Saak have published the first preprint in 2012 in the MPIMD preprint series. The preprint is entitled "A Goal-Oriented Dual LRCF-ADI for Balanced Truncation".

At the beginning of the year Judith Schneider, Martin Heß and Martin Köhler are new members of the CSC group. Additionally Patrick Kürschner and André Schneider move from Chemnitz to Magdeburg.