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News of the Research Group Computational Methods in Systems and Control Theory
News (partly german)
January 1st, 2018
emgr - EMpirical GRamian Framework version 5.3 for model reduction of input-output systems has been released. More information at: http://gramian.de
October 23rd, 2017
Martin Redmann (WIAS Berlin) and Patrick Kürschner propose error bounds for model reduction via time-limited balanced truncation.
September 15th, 2017
Peter Benner speaks in the Numerical Analysis and Scientific Computing Seminar of the Courant Institute at NYU on September 15 and in the Applied Mathematics and Scientific Computing Seminar at Temple University in Philadelphia on September 27. The topic of the talks is "Low-rank methods for PDE-constrained optimization under uncertainty".
September 11th, 2017
Petar Mlinaric, Ph.D. student in the CSC group and IMPRS Magdeburg, was selected as a new GAMM Junior in this year's competition. The GAMM Juniors represent the young scientists within the Gesellschaft für Angewandte Mathematik und Mechanik (GAMM). The appointment is for 3 years. Ten new GAMM Juniors are selected every year. Congatulations, Petar!
September 7th, 2017
This years Meeting of the GAMM activity group on applied and numerical linear algebra on September 07 and 08 in Cologne features the topic HPC. Martin Köhler and Jens Saak represented the work of the CSC group in a topical session on hybrid CPU-GPU implementations of algorithms from linear algebra.
September 1st, 2017
The MORLAB, Model Order Reduction Laboratory, toolbox version 3.0 has been released. More information at the project website: http://www.mpi-magdeburg.mpg.de/projects/morlab
August 30th, 2017
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.
August 7th, 2017
emgr - EMpirical GRamian Framework version 5.2 for model reduction of
input-output systems has been released. More information at: http://gramian.de
July 27th, 2017
Peter Benner hat als einer der Initiatoren ein neues Max Planck Research Network ins Leben gerufen. BigMax, das MaxNet on big-data-driven Materials Science, ist ein Kooperationsprojekt von 12 Max-Planck-Instituten und befasst sich mit der Analye großer Datenmengen im Bereich der Materialwissenschaften.
July 11th, 2017
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.
July 5th, 2017
The second Workshop on PowerAware Computing is taking place at the Max Planck conference center at Ringberg castle at the Tegernsee lake. The topics have been slightly broadened as compared to the previous instance in 2015. We have found a number of well established keynote and invited speakers.
May 18th, 2017
emgr - EMpirical GRamian Framework version 5.1 for model reduction of
input-output systems has been released. More information at:
http://gramian.de
February 13th, 2017
The 7th workshop on "Matrix Equations and Tensor Techniques" (METT-VII) will be held in Pisa, February 13-14, 2017. The METT workshop series is organized by Peter Benner, Heike Faßbender (TU Braunschweig), Lars Grasedyck (RWTH Aachen), Daniel Kressner (EPF Lausanne) Beatrice Meini (University of Pisa,local organizer of METT-VII), and Valeria Simoncini (University of Bologna). Previous workshops were held in Leipzig (2005), Chemnitz (2007), Braunschweig (2009), Aachen (2011), Lausanne (2013), and Bologna (2015).
January 11th, 2017
P. Benner, H. Faßbender, M. Hinze, R. Zimmermann, T. Stykel organize the MODRED 2017, January 11-13, 2017 at the Department of Mathematics and Computer Science (IMADA), University of Southern Denmark, Odense.
December 18th, 2016
Peter Benner was re-appointed to the editorial board of the SIAM Journal on Matrix Analysis and Applications (SIMAX). He will serve his fifth term as SIMAX editor from January 1, 2017 till December 31, 2019.
December 16th, 2016
Peter Benner has been appointed to the Editorial Board of the Electronic Transactions on Numerical Analysis (ETNA) for a period of 3 years. ETNA was one of the first community-driven efforts to establish a freely accessible and purely electronic scientific journal. It was founded at Kent State University in 1993. Since then, it is supported by Kent State, and more recently, also by RICAM in Linz.
November 14th, 2016
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.
November 10th, 2016
Peter Benner was appointed to the editorial board of the Springer journal "Advances in Computational Mathematics (ACOM)". ACOM aims to publish high quality, accessible and original articles at the forefront of applied and computational mathematics, with the clear potential for impact across the sciences. The journal places a particular emphasis on numerical methods, modeling, and simulation.
November 1st, 2016
The paper "Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems" by Peter Benner, Jing-Rebecca Li and Thilo Penzl (Numerical Linear Algebra with Applications 15(9):755-777, 2008) was named "Highly Cited Paper" by the Web of Science - it received enough citations to place it in the top 1% of the academic field of Mathematics based on a highly cited threshold for the field and publication year.
October 21st, 2016
emgr - EMpirical GRamian Framework for model reduction of input-output systems has been released in version 5.0. More information at: http://gramian.de.
October 4th, 2016
The Reduced Basis Summer School is an event organized by young scientists for young scientists. It aims at master students and PhD students in the field of Model Order Reduction.
September 28th, 2016
The final version of the manuscript has now been published open-access in AIMS Mathematics.
September 26th, 2016
Jens Saak and Martin Köhler will give a talk „Formeln für die Energiewende: Wie kann mit Mathematik Energie gespart werden?" within the series "Wissenschaft im Rathaus". Beginning: 7 pm. Venue: Altes Rathaus, Magdeburg.
September 25th, 2016
In September, 40 scientists mainly from China and Germany meet for a thorough discussion of 'Modelling, Model Reduction, and Optimization of Flows' in Shanghai. The workshop is organized by Shiwei Ma and Xin Du (U Shanghai) and Peter Benner and Jan Heiland and financed by the Centre for Chinese-German Cooperation CDZ.
September 21st, 2016
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.
September 15th, 2016
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.
July 29th, 2016
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).
July 18th, 2016
The CSC group is presenting talks by Pawan Goyal, Jan Heiland and Alexander Zuyev. Moreover, Jens Saak organizes a Minisymposium on Matrix Equations: Solvers and Applications in cooperation with Hermann Mena.
July 11th, 2016
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).
July 5th, 2016
Reproducible and replicable numerical experiments are the basic requirement for the comparability of different methods on common benchmark examples. This article by J.Fehr, J. Heiland, Ch. Himpe and J. Saak introduces the general topic, gives guidelines for good practice in the execution of such experiments in the area of model order reduction and explains basic requirements on the underlying software for its reusability in similar use cases.
June 14th, 2016
Peter Benner gives an invited lecture on
"Model Order Reduction
of Linear Stochastic Systems
Driven by Levy Noise" at the 6th Croatian Mathematical Congress in Zagreb, June 14-17, 2016. Petar Mlinaric participates with a contributed talk.
June 9th, 2016
Martin Köhler will present his results about an energy-efficient implementation of the Gauss-Jordan-Elimination scheme for linear systems with many right hand sides at the "Energy-Aware High Performance omputing" workshop. The workshop is part of the International Supercomputing Conference held in Frankfurt am Main from June 19th to June 23rd.
June 5th, 2016
The CSC group participates with 5 invited minisymposia and 1 contributed talks in the VII European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, June 5-10, 2016. Talks were presented by Peter Benner (2), Pawan Goyal, Martin Heß, Cleophas Kweyu, and Alexander Zuyev.
May 1st, 2016
In the first days of May 2016, the CSC and NDS Research Groups
gathered for their third time at Castle Ringberg in the Bavarian Alps
for a workshop entitled Computational Methods for High-Dimensional Problems.
Amongst the participants, several internationally known experts from various research fields joined the meeting.
April 28th, 2016
The M.E.S.S. developers team has released a small bugfix version of the recently published Version 1.0.
April 12th, 2016
The M.E.S.S. developers team has released version 1.0 of the LyaPack successor after a development time of alomst 8 years.
March 4th, 2016
The book: Index-aware Model Order Reduction Methods by Banagaaya, N., Alì, G., Schilders, W.H.A. has recently been published by Springer. Springer announces it as: "This is the first book on index-aware model order reduction methods. The splitting technique described in this book is computationally much more effective than existing methods Methods described for the
reduction of algebraic systems are new and widely applicable"
Events:
Open Access Day
February 16th, 2016
Going Open Access in scientific publishing has been discussed since the early 1990s and from the very beginnings, the Max-Planck-Society has been trying to foster and to shape this process. The arguments in favor and against Open Access are manifold and range from scientific over financial to moral aspects. Anyways, from the number of publication, a rise of Open Access publications is apparent so that Open Access is something every researcher should be aware of.
The local OA Ambassadors and the local librarian organized a well-attended, informative, and discursive workshop that featured talks by the dedicated Open Access activist Jon Tennant and Kai Geschuhn from the Max Planck Digital Library.
February 2nd, 2016
A recent article in the
Careers component of the
Science magazine features the career of Hermann Mena.
October 12th, 2015
Norman Lang, Jens Saak and Tatjana Stykel present a practically realizable implementation of the balanced truncation method for linear time-varying systems in terms of a differential Lyapunov equation solver based on a symmetric indefinite factorization of the solution.
October 2nd, 2015
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.
October 1st, 2015
The third workshop on Model Reduction of Parametrized Systems - MoRePaS 2015 - is taking place in Trieste, October 13-16, 2015. The workshop is co-organized by Peter Benner who is a member of the MoRePaS Executive Committee. The CSC group participates with talks given by Pawan Goyal and Alexander Zuyev as well as with posters presented by Martin Hess, Jan Heiland, Nicodemus Banagaaya, and Peter Benner.
September 21st, 2015
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.
July 17th, 2015
The article Towards the identification of heat induction in chip removing processes via an optimal control approach has been published in Volume 9, Issue 3 of the journal Production Engineering Research and Development. It covers a numerical method based on an optimal control ansatz for the solution of inverse heat conduction problems.
July 9th, 2015
The CSC research group organizes the annual GAMM ANLA workshop which takes place at the Max Planck Institute Magdeburg from 9.-10. July 2015
July 8th, 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.
July 4th, 2015
Inside the project EHFARS the Scientific Computing Team is holding their initiation workshop entitled "Power-Aware Computing PACO2015" at the MPI. The workshop aims at bringing German experts in the field and our project partners from Uruguay together in a 3 day event from July 6 to 08.
May 28th, 2015
Peter Benner, Matthias Heinkenschloss, Jens Saak, and Heiko Weichelt combine in this preprint various methods to effciently solve large-scale algebraic Riccati equations.
May 6th, 2015
This conference aims at bringing together experts in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. The conference is dedicated to Volker Mehrmann, who is a leading expert in the areas of the conference, and in a unique manner unifies expertise in the mathematical fields providing the title of this conference, on the occasion of his 60th birthday.
CSC News:
Matthias Voigt's PhD Defense
May 4th, 2015
Matthias Voigt is defending his dissertation on On Linear-Quadratic Optimal Control and Robustness of Differential-Algebraic Systemss on Monday, May 4th.
April 27th, 2015
The recently published article Riccati-based
Boundary Feedback Stabilization of Incompressible Navier-Stokes
Flows appeared in the 2nd issue of the 37th SISC volume on
pages A832-A858. The article describes efficient numerical methods
to compute a Riccati based feedback stabilization via boundary
control input for incompressible Navier-Stokes equations.
April 26th, 2015
The article On the benefits of the LDL^{T} factorization for large-scale differential matrix equation solvers will appear in volume 480 of the Elsevier journal Linear Algebra and its Applications. It covers efficient numerical methods for the solution of differential matrix equations.
April 10th, 2015
Prof. Harry Trentelman (University of Groningen, NL) will visit the CSC group April 15-17, 2015. He will present his work on "Model Reduction of Multi-Agent Systems Using Graph Partitions" in the Magdebug Lectures On Optimization and Control Series on April 16, 17h (Lukasklause).
April 4th, 2015
The article Towards the identification of heat induction in chip removing processes via an optimal control approach will appear in the journal Production Engineering Research and Development. It covers a numerical method based on an optimal control ansatz for the solution of inverse heat conduction problems.
January 28th, 2015
The CSC research group is looking for a student / research assistant to continue the work on the double and triple pendulum.
January 26th, 2015
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.
CSC News:
DAAD project "MINLP for damping optimization" for 2015-2016 approved
January 1st, 2015
The DAAD (German Academic Echange Service) project "MINLP for damping optimization" in cooperation with the J. J.
Strossmayer University in Osijek, Croatia, has been approved for the period 2015-2016. Project members are
Ninoslav Truhar,
Zoran Tomljanović,
Peter Benner,
Jonas Denißen,
Manuela Hund and
Yao Yue.
January 1st, 2015
The power-aware HPC task force of the CSC group is supported by the federal ministry for science and education for a period of two years. With the help of the strategies of the German government for the internationalization of science and research we receive an amount of almost 40 000€ for travel and workshop expenses.
December 30th, 2014
November 20th, 2014
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.
November 12th, 2014
Peter Benner, Jens Saak and M. Monir Uddin combine an approach for Balanced truncation of unstable systems with the efficient treatment of Stokes-like index-2 DAE structures and the latest techniques for implementing the low-rank ADI as well as choosing appropriate ADI shifts.
October 15th, 2014
Martin Köhler und Jens Saak have extended the already optimized methods for the solution of matrix Lyapunov equations with (quasi) triangular coefficient matrices to support accelerator devices. Thus, they have shown the main problems of using an accelerator device in the Bartels-Stewart algorithm and presented mathematical solutions for these problems.
October 7th, 2014
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.
September 24th, 2014
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 22 to 26 at the Momentum hotel Anif near Salzburg. The talks of the GAMM activity group will take place on Wednesday 24th and contain contributions by Peter Benner and Norman Lang. Also Jens Saak gives a talk in the GMA activity group 1.30 on Friday September 26.
September 23rd, 2014
Martin Köhler und Jens Saak have extended existing methods for the solution of matrix Lyapunov equations with (quasi) triangular coefficient matrices from Blas level-2 to level-3. Thus, they have optimized the exploitation of modern computer architectures and achieved acceleration of the execution by notable factors.
September 22nd, 2014
Within the Hot Topic session on Mathematics in developing countries at the Heidelberg Laureate forum, Peter Benner and Hermann Mena (University of Innsbruck) will jointly speak about their former German-Ecuadorian cooperation on simulating the spray-drift at the Ecuador-Colombian border caused by spraying herbicides to destroy coca plants. See
Max Planck Research 1/2014 for details of the project.
August 28th, 2014
The 3rd Symposium of the German SIAM Student Chapters
toke place in Magdeburg on 28.-29. of August 2014. We welcomed
guest from the other German SIAM Chapters in
Heidelberg
and
Trier. For the first time, members of the SIAM
Chapter in
Prag participated to extend the international connections.
August 5th, 2014
The article "Model Order Reduction for Systems with Moving Loads" by Peter Benner, Norman Lang and Jens Saak has been published at June 28 2014, in De Gruyter Oldenbourg: at-Automatisierungstechnik: volume 62 (7).
July 30th, 2014
Norman Lang, Hermann Mena, and Jens Saak present an LDL^{T} based version of the standard low-rank Lyapunov solvers based on ADI or Krylov subspace methods. The method allows us to avoid complex arithmetic for the solution of matrix differential equations via higher order time integration methods, as well as the a priori reduction of the number of columns in the right hand side of the arising algebraic Lyapunov equations inside of the time integration loop.
July 25th, 2014
Peter Benner, Ernesto Dufrechou, Pablo Ezzatti, Enrique S. Quintana-Orti and Alfredo Remon present an extension of the Lyapack library to solve band Lyapunov equations in CPU-GPU platforms. The approach exploits the modular structure in Lyapack, to incorporate a set of tuned routines that exploit the features of the problem and leverage the parallelism of current CPU-GPU platforms.
July 15th, 2014
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.
July 13th, 2014
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.
July 2nd, 2014
Martin Köhler and Jens Saak participate at the 8th International Workshop on Parallel Matrix Algorithms and Applications (PMAA14) from 2nd to 4th July 2014 in Lugano. Martin Köhler presented a new efficient implementation of the Bartels-Stewart Algorithm for the solution of dense generalized Lyapunov equations. Our software library
FlexiBLAS was presented by Jens Saak.
June 6th, 2014
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.
April 9th, 2014
The GAMM ANLA / MSIP workshop was coorganized by Peter Benner and brought together people from the communities of sparse recovery and matrix computations. The CSC group was represented by Ulrike Baur, Jonas Denissen, and Jan Heiland.
March 10th, 2014
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.
March 3rd, 2014
At the 9. Elgersburg Workshop M. Voigt and P. Kürschner represent the Computational Methods in Systems and Control Theory
group by two talks.
February 12th, 2014
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.
January 14th, 2014
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).
January 10th, 2014
Martin Köhler and Jens Saak publish LAPACK Working Note #284 on a plugin based BLAS implementation that allows to switch the BLAS library used by a program at runtime without the need for recompilation or the requirement for any super user privileges.
December 16th, 2013
Numerical methods for eigenvalue problems associated to alternating matrix pencils and polynomials are discussed. These problems arise in a large number of control applications for differential-algebraic equations ranging from regular and singular linear-quadratic optimal and robust control to dissipativity checking. We present a survey of several of these applications and give a systematic overview over the theory and the numerical solution methods. Our solution concept is based throughout on the computation of eigenvalues and de flating subspaces of even matrix pencils. The unified approach allows to generalize and improve several techniques that are currently in use in systems and control.
December 11th, 2013
Peter Benner, Martin Hess, and Judith Schneider organize the ModRed 2013 as dissemination workshop of the
BMBF research network
MoreSim4Nano, December 11-13, 2013, MPI Magdeburg (Germany).
CSC News:
Defense of Bachelor thesis by Björn Baran
December 10th, 2013
On December 10-th 2013 Björn Baran will defend his Bachelor thesis by the topic "Numerisches Lösen großer dünnbesetzter Matrixgleichungen in Python". The colloquium will be held in English language. It starts 13:30 in the Seminar room Prigogine at the MPI.
CSC News:
New group members
December 2nd, 2013
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.
November 19th, 2013
The M.E.S.S. software suite is the successor of the obsolete LyaPack MATLAB® toolbox for solving large scale matrix equations and related problems. The software suite consists of a new MATLAB toolbox and a separate C library C-M.E.S.S. which works independent from MATLAB. Due to the fact that many scientists use Python with NumPy and SciPy for their everyday work we want to provide the key algorithm of M.E.S.S. for them, too. In this report Björn Baran, Martin Köhler, Nitin Prasad and Jens Saak describe how to build an interface between Python and C-M.E.S.S. on top of the NumPy/SciPy-Python libraries.
November 14th, 2013
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).
October 29th, 2013
The third colloquium of the SFB/TR-96 takes place in Aachen from 29th to 30th of october. For further informations have a look at the official webpage of the
SFB/TR-96
October 21st, 2013
In this report, we implement a method for computing L_{∞}-norms for descriptor systems using structured iterative eigensolvers. In particular, the algorithm computes some desired imaginary eigenvalues of an even matrix pencil and uses them to determine an upper and lower bound to the L_{∞}-norm. We finally compare our method to a previously developed algorithm using structured pseudospectra. Numerical examples demonstrate the reliability and accuracy of the new method along with a significant drop in the runtime.
October 19th, 2013
Structure-Preserving Balancing of Matrix Pencils Arising in Linear-Quadratic
Optimal Control
Balancing is a popular method to increase the accuracy when numerically computing the eigenvalues of a matrix. The aim of this work is the
development of an algorithm that enables the balancing of even or skew-Hamiltonian/Hamiltonian matrix pencils by using structure-preserving transformations.
This is necessary to be able to use structure-exploiting algorithms to compute the eigenvalues of the balanced pencils. The algorithm should be implemented in FORTRAN 77
and tested for some benchmark examples.
Contact:
Matthias Voigt
October 19th, 2013
Fast Numerical Computation of Structured Real Stability Radii for Large-Scale
Matrices and Pencils
Stability radii are a measure for the robustness of differential or differential-algebraic equations under perturbations.
The goal of this project is to adapt existing methods in order to compute the structured real stability radius by using
an optimization procedure over structured pseudospectra.
Contact:
Matthias Voigt
October 16th, 2013
The authors combine stochastic collocation methods and Monte Carlo simulation with proper orthogonal decomposition
and apply it to a coplanar waveguide with uncertain material parameters.
October 9th, 2013
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.
October 7th, 2013
The model reduction method introduced in [Benner, P. and Schneider, A.; Balanced Truncation Model Order Reduction for LTI Systems with many Inputs or Outputs, in A. Edelmayer: Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems, 2010, ISBN/ISSN: 978-963-311-370-7] shows how to reduce linear time-invariant (LTI) continuous-time state space systems with either many inputs or many outputs using the well-known balanced truncation approach. We call this method balanced truncation for many terminals (BTMT). In this work we generalize BTMT to descriptor systems of the form
Eẋ(t) = Ax(t) + Bu(t), A, E ∈ ℝ^{n×n},B ∈ ℝ^{n×m}
y(t) = Cx(t) + Du(t), C ∈ ℝ^{p×n}, D∈ ℝ^{p×m},
where m ∈ 𝒪(n) and p ≪ n, or vice versa. We show how to obtain a reduced
order model by solving one Lyapunov equation and using the Gauss-Kronrod quadrature to compute the needed projection matrices. In particular, we discuss the case when E is singular and show numerical results.
September 20th, 2013
September 18th, 2013
Norman Lang, Jens Saak und Matthias Voigt present parts of their research results at the GMA activity group 1.30 from September 18 to September 20 at the Momentum hotel in Anif (Salzburg).
September 10th, 2013
Peter Benner is co-organizer (with Heike Faßbender, Lars Grasedyck, Daniel Kressner) of the 5th Workshop on Matrix Equations and Tensor Techniques, October 10-11, 2013, EPF Lausanne (Switzerland).
September 9th, 2013
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.
August 26th, 2013
The next workshop of the GAMM activity group ”Dynamics and Control Theory“ will take place at the MPI Magdeburg from 09/26 - 09/27/2013. The local organizer and contact is Matthias Voigt.
July 29th, 2013
Skew-Hamiltonian/Hamiltonian matrix pencils λS - H appear in many applications, including linear quadratic optimal control problems, H_{∞}-optimization, certain multi-body systems and many other areas in applied mathematics, physics, and chemistry. In these applications it is necessary to compute certain eigenvalues and/or corresponding deflating subspaces of these matrix pencils. Recently developed methods exploit and preserve the skew-Hamiltonian/Hamiltonian structure and hence increase reliability, accuracy and performance of the computations. In this paper we describe the corresponding algorithms which have been implemented in the style of subroutines of the Subroutine Library in Control Theory (SLICOT). Furthermore, we address some of their applications. We describe variants for real and complex problems with versions for factored and unfactored matrices S.
July 29th, 2013
In this paper we describe the implementation of the algorithms in the style of subroutine included in the Subroutine Library in Control Theory (SLICOT) described in Part I of this work and address various details. Furthermore, we perform numerical tests using real-world examples to demonstrate the superiority of the new algorithms compared to standard methods.
July 26th, 2013
Peter Benner is member of the scientific committee of the ENUMATH 2013, August 26-30 2013, EPFL Lausanne (Switzerland). Martin Stoll, Peter Benner will give minisymposia, and H. Yücel, Y. Zhang and Martin Heß contributed talks.
July 1st, 2013
June 27th, 2013
We explore the Tractability Index of Differential Algebraic Equations (DAEs) that emerge in the simulation of gas transport networks. Depending on the complexity of the network, systems of index~1 or index~2 can arise. We then apply Model Order Reduction (MOR) techniques such as Proper Orthogonal Decomposition (POD) to a network of moderate size and complexity and show that one can reduce the system size significantly. This can be either achieved by directly reducing the original DAE~formulation or by applying MOR to an index-reduced system. First numerical results are reported on.
June 26th, 2013
We consider the efficient solution of the modified Cahn-Hilliard equation for binary image inpainting using convexity splitting, which allows an unconditionally gradient stable time-discretization scheme. We look at a double-well as well as a double obstacle potential. For the latter we get a nonlinear system for which we apply a semi-smooth Newton method combined with a Moreau-Yosida regularization technique. At the heart of both methods lies the solution of large and sparse linear systems. We introduce and study block-triangular preconditioners using an efficient and easy to apply Schur complement approximation. Numerical results indicate that our preconditioners work very well for both problems and show that qualitatively better results can be obtained using the double obstacle potential.
June 26th, 2013
The solution of time-dependent PDE-constrained optimization problems is a challenging task in numerical analysis and applied mathematics. All-at-once discretizations and corresponding solvers provide efficient methods to robustly solve the arising discretized equations. One of the drawbacks of this approach is the high storage demand for the vectors representing the discrete space-time cylinder. We here introduce a low-rank in time technique that exploits the low-rank nature of the solution. The theoretical foundations for this approach originate in the numerical treatment of matrix equations and can be carried over to PDE-constrained optimization. We illustrate how three different problems can be rewritten and used within a low-rank Krylov subspace solver with appropriate preconditioning.
June 24th, 2013
Efficient numerical algorithms for the solution of large and sparse matrix Riccati and Lyapunov equations based on the low rank alternating directions implicit (ADI) iteration have become available around the year 2000. Over the decade that passed since then, additional methods based on extended and rational Krylov subspace projection have entered the field and proved to be competitive alternatives. In this survey we sketch both types of methods and discuss their advantages and drawbacks. We focus on the continuous time case here, but corresponding results for discrete time problems can for most results be found in the available literature and will be referred to throughout the paper.
June 24th, 2013
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.
CSC News:
CSC at Preconditioning 2013
June 16th, 2013
The CSC group is participating at this years Preconditioning meeting in Oxford, UK. Jessica Bosch and Andrew Barker are giving contributed talks and Martin Stoll is giving a plenary lecture. Additionally.
Andrew will spend the week prior to the meeting at OCCAM collaborating with John Pearson (Oxford) and Tyron Rees (RAL).
June 10th, 2013
Peter Benner is member of the organizing committee of the European Conference on Computational Optimization (EUCCO), July 17-19, 2013, Chemnitz, Germany.
CSC News:
New intern
June 6th, 2013
Ryan Lowe from Queen's University in Kingston starts as an intern and will investigate a new approach for the computation of the L
_{∞}-norm for descriptor systems of high dimension. The internship is funded by a grant from the
DAAD RISE program.
CSC News:
New intern
May 21st, 2013
Thomas Hughes from the Queen's University at Kingston starts as intern and will investigate efficient techniques for ℋ_{2} model reduction of bilinear systems.
May 10th, 2013
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.
May 8th, 2013
Studies on the low-rank ADI for large-scale Stein equations
Contact:
Patrick Kürschner
CSC News:
New intern
May 8th, 2013
Deepak Matcha Venkat from IIT Bombay starts as anintern and will investigate the two-degree of freedom control of the double and triple pendulum.
May 3rd, 2013
Peter Benner and Patrick Kürschner present new results and numerical
enhancements for the low-rank ADI iteration for large-scale Sylvester matrix equations.
May 2nd, 2013
The Computational Methods in Systems and Control Theory group is proud to welcome Dr. Alfredo Remón as a new group member. Dr. Remón has been a long term cooperation partner of the group in the field of Multicore and GPU Computing. He received his PhD in the group of Prof. E. Quintana-Ortí at UJI Castellon (Spain)
April 24th, 2013
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.
CSC News:
New student assistant and diploma candidate
April 1st, 2013
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.
CSC News:
New student assistant and Bachelor candidate
April 1st, 2013
On April 1st Björn Baran started as a new student research assistant in the M.E.S.S. project. His main duties will be the implementation of recent algorithmic advances in the Matlab version. In his Bachelor thesis he will then port these new codes to Python and compare this implementation with simple python interface functions to the C version of M.E.S.S.
March 15th, 2013
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.
March 11th, 2013
Heiko Weichelt presented his latest results about
Riccati-Based Boundary Feedback Stabilization of Multi-Field Flow Problems at the OCIP2013 in Garching by Munich (Germany).
CSC News:
Jonas Denißen visits J. J. Strossmayer University of Osijek in Croatia
March 10th, 2013
Jonas Denißen visits the J. J. Strossmayer University of Osijek, Department of Mathematics, Osijek, Croatia in the period March 10 - 17, 2013. The purpose of his stay is to work with
Zoran Tomljanović on the DAAD project
"Optimal damping of vibrating systems".
February 24th, 2013
The final meeting of the DFG SPP1253 Optimization with Partial Differential Equations was held at Banz monastery.
Peter Benner, Heiko Weichelt and
Jens Saak participated and presented the latest results of the local project
Optimal Control-Based Feedback Stabilization of Multi-Field Flow Problems there.
(Talk ca. 16MB as PDF)
CSC News:
New group member
February 18th, 2013
The Computational Methods in Systems and Control Theory group is proud to welcome Dr. Zvonimir Bujanovic as a new group member. Dr. Bujanovic revieved his PhD degree from University of Zagreb under the supervision of Prof. Zlatko Drmac.
February 14th, 2013
A book: System-level Modeling of MEMS edited by Tamara Bechtold, Gabriele Schrag and Lihong Feng is published in January, 2013 by WILEY-VCH. This book is a volume of the series: Advanced Micro & Nanosystems edited by Brand, Fedder, Hierold, Korvink and Tabata.
February 11th, 2013
On this years Elgersburg Workshop the Computational Methods in Systems and Control Theory is presenting three talks by P. Benner, M. Redmann and M.Voigt. Additionally, U. Baur, T. Breiten, J. Denißen and J. Saak are participating.
February 5th, 2013
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".
CSC News:
New intern
February 5th, 2013
Sandra Kutz (student of applied mathematics at OvGU) is investigating the capabilities and limitations of Matlabs GPU computing toolbox in the context of solvers for large and sparse matrix equations during a 5 week internship.
January 31st, 2013
A meeting of the working group parameterization and simulation of the SFB/TR-96 takes place in Dresden from 31st of January to 1st of February. For further informations have a look at the official webpage of the
SFB/TR-96
January 21st, 2013
Peter Benner and Wolfgang Hackbusch (MPI Leipzig) are (co-)organizing the GAMM Seminar Numerical Methods for Uncertainty Quantification at the MPI for Mathematics in the Sciences Leipzig, Germany. Martin Heß, Ulrike Baur, Akwun Onwunta, Kapil Ahuja and Martin Redmann from the CSC group will also participate.
New appointments:
Jessica Bosch, Mian Ilyas Ahmad, Andrew Barker, Yao Yue join the CSC group
January 7th, 2013
The CSC group is proud to welcome Mian Ilyas Ahmad (Nust, Pakistan), Andrew Barker (LSU, USA), Yao Yue (Leuven, Belgium) as postdocs and Jessica Bosch (Oxford, UK) as a PhD student.
December 20th, 2012
We consider the effcient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At the heart of this method lies the solution of large and sparse linear systems for which we propose the use of preconditioned Krylov subspace solvers using an effective Schur complement approximation. Numerical results illustrate the competitiveness of this approach.
CSC News:
DAAD project for 2013-2014 approved
December 19th, 2012
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.
December 18th, 2012
Model order recuction using balanced truncation for differential algebraic second order systems in M.E.S.S.
Contact:
Jens Saak
December 18th, 2012
Numerical Solution of large and sparse matrix equations on distributed memory parallel machines
Contact:
Jens Saak
December 18th, 2012
Approximate solution of the Linear systems of equations in the ADI Method for large and sparse matrix equations
Contact:
Jens Saak
December 18th, 2012
A CG-Method with ADI preconditioning for the solution of large sparse Lyapunov equations with symmetric coefficient matrices
Contact:
Jens Saak
December 18th, 2012
Step size control for the numerical solution of large and sparse matrix differential Riccati equations
Contact:
Jens Saak
December 18th, 2012
Numerical solution of large sparse Matrix equations on CUDA GPUs
Contact:
Jens Saak
December 18th, 2012
Numerical solution of large and sparse matrix equations in Python
Contact:
Jens Saak
Events:
Scientific Network: Scale bridging simulation methods based on order-reduction and co-simulation, 10.-12. Dezember
December 4th, 2012
Judith and André Schneider will participate in the Kickoff Meeting of the Scientific Network at TU Darmstadt.
November 20th, 2012
The article Computation of a Compact State Space Model for an Adaptive Spindle Head Configuration with Piezo Actuators using Balanced Truncation will appear in volume 6 issue 6 of the Springer journal Production Engineering Research and Development. It covers efficient numerical methods for the model order reduction of the resulting index 1 differential algebraic systems via balanced truncation.
November 8th, 2012
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.
November 8th, 2012
On Thursday November 08 and Friady November 09 Heiko Panzer and Thomas Wolf from "Lehrstuhl für Regelungstechnik" (Prof. B. Lohmann) at TU Munich will be visiting CSC. In a seminar double feature on Friday at 10 (V0.05 2+3) they will present their work on "ADI for Lyapunov Equations by Krylov Subspace Methods and a New Formulation of the Residual" and "On Strictly Dissipative State Space Realizations of Second Order Systems".
October 24th, 2012
The second colloquium of the SFB/TR-96 takes place at Fraunhofer IWU in Chemnitz from 24th to 25th of october. For further informations have a look at the official webpage of the
SFB/TR-96
October 19th, 2012
The authors show a method for boundary feedback stabilization of the Stokes around a stationary trajectory using a new non-conforming
finite element method that represents the action of the Leray projection pointwise locally.
October 15th, 2012
Prof. Dr. Sebastian Schöps from
TU Darmstadt and
Daniel Schmidthäusler from Bergische Universität Wuppertal visit the CSC group on October the 15th and 16th. They will give seminar talks about "Uncertainties in Magnetoquasistatic Field Problems" and "Reduction of Linear Subdomains for Non-linear Electro-quasistatic Field Simulations" on October 16th, 3:15pm (V0.05-2+3).
October 8th, 2012
The reduced basis method (RBM) generates low order models for the solution of parametrized partial differential equations (PDEs) to allow for efficient evaluation in many-query and real-time contexts. We show the theoretical framework in which the RBM is applied to Maxwell's equations and present numerical results for model reduction in frequency domain. Using rigorous error estimators, the RBM achieves low order models under variation of material parameters and geometry. The RBM reduces model order by a factor of 50 to 100 and reduces compute time by a factor of 200 and more for numerical experiments using standard circuit elements.
October 8th, 2012
Peter Benner is member of the organizing and scientific committees of the CIRM workshop Structured Matrix Computations in Non Euclidean Geometries: Algorithms and Applications. It is held from October 8-12, 2012 in CIRM Luminy. Peter Benner and Matthias Voigt will present their work in contributed talks.
October 2nd, 2012
Peter Benner is member of the executive and scientific committees for the Second International Workshop on Model Reduction for Parametrized Systems (MoRePaS II) which is held in Schloss Reisensburg, Günzburg, Germany from October 2-5, 2012. Sara Grundel and Ulrike Bauer will give a contributed talk and participate in the poster session, respectively.
September 27th, 2012
Swing up and stabilization of the inverse double- and triplependulum. Contact:
Patrick Kürschner.
This news entry is expired.
September 25th, 2012
The Chemitz FEM Symposium is celebrating a triple jubilee this year. At the 25th symposium Arnd Meyer and Ulrich Langer are celebrating their 60th birthdays. The CSC group is congratulating and sends Peter Benner, Jens Saak(poster presentation) and Piotr Skrzypacz (talk) to participate in the event.
September 20th, 2012
PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs.
September 19th, 2012
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.
September 17th, 2012
Heiko Weichelt will present his latest results on the annual meeting of the
Deutschen Mathematiker Vereinigung that takes place in Saarbrücken, Germany, from 17th til 20th of September 2012.
September 17th, 2012
Peter Benner, Jens Saak und Martin Stoll are visiting the kick-off meeting of GAMM activity group Computational Science and Engineering (CSE) in Garching on September 17th and 18th.
September 10th, 2012
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.
September 2nd, 2012
From September 2nd to 5th the 12th GAMM Workshop on Applied and Numerical Linear Algebra is taking place on Chateau Liblice in Czech Republic. The CSC group will give talks by Jens Saak, Kapil Ahuja, and Heiko Weichelt.
July 27th, 2012
The slides of the talks and the group photo taken on the balkony are now available following the link above. Workshop patricipants may request user and password for access to the archive from the research group members.
CSC News:
Linux cluster otto now computing faster
July 20th, 2012
The Linux cluster
otto that was installed at the institute last year was extended during the week from july 16. to july 20. The user can now access 90 equal compute nodes based on Intel Xeon Westmere CPUs and an overall memory of 4,32TB. The current installation is now providing a theoretical peak performance of 11.5 TFlops (11.5 trillion floating point operations per second). The effective practical performance was measured using the LINPACK Benchmark that is also used for the TOP500 (http://www.top500.org) ranking of fastest super computers in the world. Here the updated system reached a measured performance of 10.36TFlops, which corresponds to 90.1% of the theoretic peak performance. Furthermore 16 AMD Opteron based nodes deliver an additional 2.2TFlops compute capacity.
The cluster is supporting the work of all research groups at the institute. With its help many experiments and molecules can be simulated that would not have been doable on a standard workstation, or that
would have require unacceptable execution times. The research group Computational Methods in Systems and Control Theory that is in charge of the device, is using the cluster to develop parallel numerical algorithms for model reduction and optimal control.
New Team Members:
Martin Redmann, Piotr Skrzypacz
July 1st, 2012
The CSC group welcomes two new team members. Martin Redmann joined us as a PhD student working on the interface of model order reduction and stochastics. Dr. Piotr Skrzypacz joined the CSC group as a Postdoc for the remainder of this year.
June 29th, 2012
John Pearson (University of Oxford) will be coming to Magdeburg in September and October of 2012. He will be working with Martin Stoll on the fast solution
of optimal control problems coming from the modelling of chemical processes. His research visit is kindly funded by the
ESF OPTPDE program. This visit
is part of an ongoing
project between Oxford and Magdeburg.
June 20th, 2012
June 18th, 2012
Dr. Vasile Sima from the National Institute for Research & Development in Informatics, Bucharest, Romania, visits CSC in the period June 18 - July 20, 2012.
June 16th, 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.
June 12th, 2012
One Postdoctoral Research Associate in Numerical Analysis working with Dr. Martin
Stoll within the Computational Methods in Systems and Control Theory group. Our
goal is the fast solution of large-scale optimization problems subject to a partial
differential equation (PDE) or systems of PDEs with possibly additional algebraic
or box constraints. This news entry is expired.
June 12th, 2012
One Postdoctoral Research Associate in Numerical Analysis working with Prof. Peter Benner
within the Computational Methods in Systems and Control Theory group. The research focus in this project is on developing novel model order reduction
techniques for nonlinear systems. This news entry is expired.
June 12th, 2012
One Senior Postdoctoral Research Associate in Numerical Analysis working with Prof. Peter Benner
within the Computational Methods in Systems and Control Theory group. The
candidate is expected to develop computational methods for UQ in applications
arising in process engineering, systems biology, biotechnology, and other areas of
science and engineering with a focus on the research fields at the MPI MD. This news entry is expired.
May 16th, 2012
extension and maintenance of the research groups web site. Contact:
Jens Saak.
This news entry is expired.
Events:
Workshop on Nonlinear Model Order Reduction
May 6th, 2012
The workshop will be held at
Schloss Ringberg. The program including abstracts of the presentations can be downloaded
here.
April 25th, 2012
Nick Higham from the University of Manchester will be visiting the CSC group from the 25th of April. Nick will give a presentation as part of the MPI
colloquium series joint with the Department of Mathematics colloquium series. The title of his presentation is Recent Progress in Matrix Functions and the talk will be given on Thursday, April 26, 2012 at 5 pm here at the MPI.
Nick is the Richardson Professor of Applied Mathematics and an expert on many things in Numerical Analysis with a particular focus on Numerical Linear Algebra as well as Numerical Software. He is the vice president
of SIAM, a fellow of the Royal Society and SIAM fellow.
April 18th, 2012
Jan Heiland from TU Berlin will be visiting the CSC group. He will give a presentation titled
Differential-algebraic Riccati Decoupling in Optimal Control of Flows in the CSC
Reading Group. Main reason for the visit is a projected collaboration with Jens Saak, Norman Lang and Heiko Weichelt.
April 9th, 2012
Catherine Powell from the University of Manchester will be visiting the CSC group after Easter. She will give a presentation titled Efficient solvers for saddle point problems with random data on Tuesday the 10th of April at 2pm. Catherine is an expert on Uncertainty Quantification with a particular
focus on computational fluid dynamics.
CSC News:
Three Interns Working with CSC
April 2nd, 2012
Starting from May, three interns will visit CSC for two to three months. Kumod Ranjan (
National Institute of Technology, Warangal (India)) who got a
DAAD WISE scholarship will assist Jens Saak with his work. Furthermore, Peihong Jiang (
University of Rochester (USA)) who
received a grant from the
DAAD RISE program and Maximilian Bremer (
University of Texas at Austin (USA)) will join Matthias Voigt.
CSC News:
MPCSC at GAMM Annual Meeting in Darmstadt
March 30th, 2012
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.
March 29th, 2012
The 12th Copper Mountain Confernce on Iterative Methods will take place from 25th till 30th March 2012. Heiko Weichelt will present the latest results about Efficient Solution of Large-Scale Saddle Point Systems
Arising in Feedback Control of the Stokes Equations there.
March 21st, 2012
Elisabeth Ullmann (University of Bath) is visiting us this week. She gives a seminar talk on
Numerical Methods for PDEs with Uncertainties (21/03/11, 14:00).
March 19th, 2012
This paper presents the results obtained within the
FVV pilot study concerning model order reduction for EMBS.
March 13th, 2012
Heiko Weichelt presented his latest results about
Riccati-Based Boundary Feedback Stabilization of Incompressible Flow Problems at the OCIP2012 in Garching by Munich (Germany).
March 6th, 2012
In this paper we consider a PDE-constrained optimization problem where an H1 regularization control term is introduced. We address both time-independent and time-dependent versions. We introduce bound constraints on the state, and show how these can be handled by a Moreau-Yosida penalty function. We propose Krylov solvers and preconditioners for the different problems and illustrate their performance with numerical examples.
March 1st, 2012
In March Kapil Ahuja, who received a PhD from Virgina Tech (Blacksburg) last year, is new in the CSC group.
February 28th, 2012
We investigate the application of the LR Cholesky algorithm to symmetric hierarchical matrices. The data-sparsity of these matrices make the otherwise expensive LR Cholesky algorithm applicable, as long as the data-sparsity is preserved. We will see that the data-sparsity of hierarchical matrices is not well preserved.
We will explain this behavior by applying a theorem on the structure preservation of diagonal plus semiseparable matrices under LR Cholesky transformations.
January 24th, 2012
Kalman-Yakubovich-Popov Lemma for Algebraic Difference Equations
In many fields of systems and control theory, dynamical systems are analyzed via certain rational
matrix functions (so-called Popov functions). Properties of Popov functions can often be characterized
via solvability of linear matrix inequalities. The aim of this thesis is the adaption of the existing
theory to the case that the dynamical system is given as algebraic difference equation. Furthermore,
relations to the structure of palindromic matrix pencils should be analyzed. Optionally, applications
of the theory can be taken into account, e.g., for the structure analysis of dynamical systems or
optimal control.
Contact:
Matthias Voigt
January 24th, 2012
Numerical Computation of Generalized Structured Pseudospectra
For the analysis of the properties of matrices often their pseudospectra are considered.
For the visualization of pseudospectra a MATLAB GUI has already been developed. For the
graphical depiction of structured pseudospectra, a generalization of pseudospectra of matrices,
such a tool does not exist. Therefore, the task of this thesis is to develop methods for the computation
of structured pseudospectra and to implement these in MATLAB. In particular, different approaches for
the acceleration of the computations should be analyzed.
Contact:
Matthias Voigt This news entry is expired.
January 23rd, 2012
Compute the subgradient of the spectral abscissa numerically.Contact:
Sara Grundel
January 23rd, 2012
Model reduction in complex biochemical networksAn important tool in the analysis of complex physical phenomena is the
simulation of the underlying mathematical models, which are often given
by systems of ordinary and/or partial differential equations. As one
is interested in models as accurate as possible, linear models are often
insufficient such that one is faced with large-scale nonlinear systems.
Frequently, these cannot be handled efficiently, necessitating model order
reduction, i.e., the construction of a smaller system approximating the
original one. In this thesis, a recently introduced approach for nonlinear model reduction should be implemented and tested
by means of a real-life application arising in the context of biochemical reaction networks.
Contact:
Tobias Breiten
Thesis Topic:
Bachelor Thesis
January 19th, 2012
This thesis deals with the study and implementation of shooting methods for PDE-constrained optimization problems. This approach will combine the numerical analysis of ODEs with efficient techniques used in numerical linear algebra.
Contact:
Martin Stoll
January 19th, 2012
Optimal Control of a second order partial differential
equation with acceleration measurements. Optimal control problems for
infinite dimensional second order systems with acceleration measurements are
in general ill-posed. Jacob and Morris proposed a method exploiting the actual
implementation of the measurement that pulls the problem back to a well posed
one. Here such a system is to be implemented and solved
numerically.
Contact:
Jens Saak
January 18th, 2012
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
January 18th, 2012
Simultaneous iterative solution of the adjoint linear systems in the dual low-rank ADI iteration for Lyapunov equationsSolving 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
January 16th, 2012
Bart Vandereycken is visiting from EPFL from the 16th to the 20th of January. Bart will give a talk titled "Riemannian algorithms for rank-structured matrices and tensors" on Tuesday at 2pm. Please come along. Bart is the recipient of the 2011 Householder prize, which is awarded only every 3 years. He is an expert on optimization on manifolds and matrix equations.
January 16th, 2012
Hermann Mena (ENP Quito, Ecuador) is visiting the MPI Magdeburg again for three weeks.
January 11th, 2012
Michael Saunders is visiting the CSC group from Stanford. He will give a presentation on Thursday at 2pm at the MPI titled "CG and MINRES: A tale of two solvers". Michael is an expert on numerical optimization and numerical linear algebra among other things. He is an ISI highly cited researcher in both mathematics and computer science. He will arrive on Wednesday and stay until Sunday.
January 9th, 2012
In January Akwum Onwunta started as PhD-student in the CSC group.
January 5th, 2012
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".
December 19th, 2011
The CSC group published 3 new preprints in the last 5 days:
- Peter Benner, Tobias Breiten: On optimality of interpolation-based low-rank approximations of large-scale matrix equations
- Peter Benner, Martin Köhler, Jens Saak: Sparse-Dense Sylvester Equations in ℋ₂-Model Order Reduction
- Thomas Mach, Jens Saak: Towards an ADI iteration for Tensor Structured Equations
November 21st, 2011
This workshop is the fourth in a series of workshops on matrix equations held previously in Leipzig 2005, Chemnitz 2007, and Braunschweig 2009. The workshops are organized by Peter Benner (MPI Magdeburg), Heike Fassbender (TU Braunschweig), Lars Grasedyck (RWTH Aachen), and Daniel Kressner (EPF Lausanne).
New visitor:
John Pearson visiting from Oxford
November 14th, 2011
John Pearson is visiting the CSC group from the 14th to the 18th of November. He is giving a seminar titled Preconditioned Iterative Methods for Optimal Control Problems on Thursday the 17th at 3pm. He will also be working with Martin Stoll on the fast solution of nonlinear optimal control problems.
CSC News:
Philip Losse's PhD Defense
November 4th, 2011
Philip Losse defended his dissertation on The ℋ_{∞} Optimal Control Problem for Descriptor Systems on Friday, 4th November. He will receive his degree from TU Chemnitz.
November 1st, 2011
Cosmin Ionita from Rice University, Houston is visiting the CSC group. He will give a seminar talk on November 24th.
October 10th, 2011
The Summer School Numerical Linear Algebra for Dynamical and High-Dimensional Systems will be held on October 10-15, 2011 in Trogir, Croatia and is organized by Peter Benner (MPI Magdeburg), Daniel Kressner (EPF Lausanne), Ninoslav Truhar (University of Osijek) and Zlatko Drmač (University of Zagreb).
October 4th, 2011
On October 4th and 5th all members of the DFG Transregio SFB 96
Thermo-energetic design of machine tools meet at TU Dresden for their first general assembly. During the 2 days workshop the 19 participating subprojects present their current and future work for the first year of existence. Peter Benner, Norman Lang and Jens Saak will join as responsible for project A06
Model Order Reduction for Thermo-Elastic Assembly Group Models and establish contacts to the persons in charge of the other simulation projects.
October 1st, 2011
In October Sara Grundel, who received a PhD from the Courant Institute (New York) in May, and Norman Lang (joining the Chemnitz part) are new in the CSC group.
September 25th, 2011
The anual meeting of the DFG SPP1253 Optimization with Partial Differential Equations will be held at Banz monastery.
Peter Benner, Heiko Weichelt and
Jens Saak will participate and present the latest results of the local project
Optimal Control-Based Feedback Stabilization in Multi-Field Flow Problems there.
(Talk)
September 22nd, 2011
The
GAMM Workshop 2011 on Applied and Numerical Linear Algebra with Special Emphasis on Model Reduction will be held in Bremen on 22 and 23 September 2011.
Peter Benner is member of the organizing committee. Tobias Breiten, Patrick Kürschner, Thomas Mach, Jens Saak, and André Schneider present their work in contributed talks. The workshop is followed by a
special colloquium celebrating the 60th birthday of Angelika Bunse-Gerstner.
September 15th, 2011
In September Mohammed Sahadet Hossain, who recently finished his PhD in Chemnitz, and the PhD-students Yongjin Zhang and Jonas Denißen are new in the CSC group.
September 14th, 2011
In this article, we motivate, derive and test effective preconditioners to be used with the minres algorithm for solving a number of saddle point systems, which arise in PDE constrained optimization problems. We consider the distributed control problem involving the heat equation with two different functionals, and the Neumann boundary control problem involving Poisson equation and the heat equation. Crucial to the effectiveness of our preconditioners in each case is an effective approximation of the Schur complement of the matrix system. In each case, we state the problem being solved, propose the preconditioning approach, prove relevant eigenvalue bounds, and provide numerical results which demonstrate that our solvers are effective for a wide range of regularization parameter values, as well as mesh sizes and time-steps.
August 22nd, 2011
The 17th ILAS Conference will be held in Braunschweig from 22 to 26 august 2011. Peter Benner is member of the organizing committee. Jens Saak and Alfredo Remón Gómez (Universitat Jaume I, Castelló de la Plana) are organizing an YR minisymposium on Parallel Computing in Numerical Linear Algebra. Further several group members will give contributed talks.
August 1st, 2011
Since August Mohammad Monir Uddin is PhD-student of the CSC group.
New visitor:
Fikriye Yilmaz (Gazi University, Ankara) visiting
July 25th, 2011
Fikriye Yilmaz from Gazi University in Ankara is visiting the CSC group. She is going to work with Martin Stoll on optimal control problems for PDEs and is giving a presentation in the
CSC seminar on Wednesday at 11 am. The title for her talk is "All-at-once solution of optimal control for Burgers equation"
July 19th, 2011
In this paper we describe the efficient solution of a PDE-constrained optimization problem subject to the time-periodic heat equation. We propose a space-time formulation for which we develop a monolithic solver. We present preconditioners well suited to approximate the Schur-complement of the saddle point system associated with the first order conditions. This means that in addition to a Richardson iteration based preconditioner we also introduce a preconditioner based on the tensor product structure of the PDE discretization, which allows the use of a FFT based preconditioner. We also consider additional bound constraints that can be treated using a semi-smooth Newton method. Moreover, we introduce robust preconditioners with respect to the regularization parameter. Numerical results will illustrate the competitiveness and flexibility of our approach.
July 7th, 2011
Regulator based tracking control of a parabolic partial
differential equation under control constraints
We are searching for a regulator based feedback control u.
Since this is not covered by the linear quadratic regulator approach,
we first compute a reference pair of control and solution trajectory via
open loop optimization. The resulting pair is then tracked by the regulator
based feedback control.
Contact:
Jens Saak
July 6th, 2011
extension and maintenance of the research groups web site. Contact:
Jens Saak.
This news entry is expired.
July 6th, 2011
Further development of the software library
M.E.S.S. Contact:
Martin Köhler.
This news entry is expired.
July 5th, 2011
Model reduction is a crucial and important technique in many applications such as chemical or mechanical engineering. Important contributions have been made over the last decades and today much of the research is devoted to developing techniques for generating reduced order models for parameter dependent problems. The Computational Methods in Systems and Control Theory group at the MPI Magdeburg and the RWTH Aachen (research groups of
Martin Grepl and
Karen Veroy-Grepl) are joining forces for a day,
5th of July 2011, to discuss the latest developments and state-of-the art methods to generate accurate and efficient reduced models for problems coming from a variety of applications. The workshop is going to be held in our big seminar room and we invite you to join us for the whole day or parts of it.
For more information see the
workshop webpage or contact Martin Stoll (stollm@mpi-magdeburg.mpg.de).
July 1st, 2011
Deutsche Forschungs Gemeinschaft (DFG) sets up new Transregio SFB 96
Thermo-Energetic Design of Machine Tools at Technical Universities Dresden and Chemnitz, as well as RWTH Aachen. The Chemnitz part of our research group is participating with project A06
Model Order Reduction for thermo-elastic assembly group models.
July 1st, 2011
For the research project
"Model Order Reduction for Thermo-Elastic Assembly Group Models" we have an open full researcher position following group 13 in TV-L in the Chemnitz part of our group. Please find details in the
job posting at Chemnitz UT math faculty. Applications due July 8th 2011.
This news entry is expired.
June 27th, 2011
Dr. Vasile Sima from the National Institute for Research & Development in Informatics, Bucharest, Romania, will visit CSC in the period June 27 - July 26, 2011.
June 23rd, 2011
The main topic of the proposed dissertation is to develop and implement efficient iterative solvers for the numerical solution of Cahn-Hilliard problems. Please note that the description is in German but if you
are interested anyway, please contact Martin Stoll (stollm@mpi...) for more details. This topic is already taken but similar ones can be offered for interested students. This news entry is expired.
June 12th, 2011
Peter Benner and Martin Stoll will participate in the
Householder Symposium XVIII on Numerical Linear Algebra to be held on June 12-17, 2011, at the Granlibakken Conference Center & Lodge in Tahoe City, California. In his plenary lecture Peter Benner will talk about
Rational Krylov Subspaces for Nonlinear Model Reduction. Martin Stoll will present a poster on
Preconditioning for time-dependent optimal control problems.
The Householder Symposia are one of the longest running conference series in applied mathematics and attendance is by invitation only. The first meeting goes back to 1961 in Gatlinburg and therefore, the first meetings were called
Gatlinburg Conference. The series was renamed in 1969 to honor Alston Householder for his groundbreaking contributions to Numerical Mathematics and is now held every 3 years.
June 11th, 2011
Peter Benner is member of the organizing committee for a 1-day symposium on Eigenvalues, Model Order Reduction and Trust Regions in celebration of Danny Sorensen's 65th birthday. The symposium will be held in Reno, Nevada.
June 8th, 2011
We discuss the problem of ℋ₂-model order reduction of bilinear control systems. We revisit existing first order necessary conditions for ℋ₂-optimality based on the solutions of generalized Lyapunov equations arising in bilinear system theory and present an iterative algorithm which, upon convergence, yields a reduced system fulfilling these conditions. We further establish a connection to another method based on generalized rational interpolation leading to an adaption of the successful iterative rational Krylov algorithm (IRKA) to bilinear systems.
June 8th, 2011
The solution of time-dependent PDE-constrained optimization problems subject to unsteady flow equations presents a challenge to both algorithms and computers. In this paper we present an all-at-once approach where we solve for all time-steps of the discretized unsteady Stokes problem at once. The most desirable feature of this approach is that for all steps of an iterative scheme we only need approximate solutions of the discretized Stokes operator. This leads to an efficient scheme which exhibits mesh-independent behaviour.
June 1st, 2011
Test sequence for the verification of a MATLAB/Fortran function implementation. Contact:
Matthias Voigt,
more informations (german only).
This news entry is expired.
May 28th, 2011
Saturday, 28th May 2011, 6.00 a.m. to 1.00 p.m., Max Planck Institute Magdeburg We cordially invite you and your family to discover basic research in the engineering sciences: during guided tours through our institute, short lectures on our research topics and in experiments for kids and grown-ups! Our program for you (in German)
...
May 26th, 2011
Newsropa.de have an article on our new Linux-cluster otto. Further the Volksstimme have an article in their print-version on otto.
May 25th, 2011
The registration for the Summer School Numerical Linear Algebra for Dynamical and High-Dimensional Systems is now open until June 30. The school will be held on October 10-15, 2011 in Trogir, Croatia and is organized by Peter Benner (MPI Magdeburg), Daniel Kressner (EPF Lausanne), Ninoslav Truhar (University of Osijek) and Zlatko Drmač (University of Zagreb).
May 16th, 2011
Roland Herzog (TU Chemnitz) and
Martin Stoll are organizing a minisymposium on
Preconditioning in PDE-Constrained Optimization at the SIAM Conference on Optimization, which takes place from May 16 until May 19, 2011, in Darmstadt. Peter Benner gives a talk in the minisymposium
Model Order Reduction Techniques in PDE Constrained Optimization on
System-theoretic Methods for Model Reduction of Linear and Nonlinear Parabolic Systems, too.
CSC News:
Daniel Kressner visiting
May 11th, 2011
Daniel Kressner (
EPF Lausanne) is visiting us 11th to 13th of May. He will talk about
Low-rank tensor techniques for parametrized and high-dimensional linear algebra problems in the
MPI Colloquium on the
12th of May. Daniel is an expert on many things in numerical linear algebra such as tensor techniques and eigenvalue problems.
CSC News:
David Knezevic visiting
May 9th, 2011
David Knezevic (MIT) will be visiting us from the 9th to the 11th of May. David is an expert on the analysis and implementation of the Certified Reduced Basis Method. He is one of the developers of the finite element package libmesh. His PhD at Oxford was on the numerical simulation of dilute polymeric fluids. David gives a seminar talk on
The Certified Reduced Basis Method: Real-time Simulation of Parametrized Systems (05/09/11, 15:30).
May 6th, 2011
Friday, May 6th, 2011, 9.00 a.m. to 1.00 p.m., Max Planck Institute Magdeburg We would like to discuss with you how to enhance cooperation between fundamental research and industrial application, looking at projects which are being pursued jointly between research groups of the Max Planck Institute Magdeburg and external partners from industry. Invitation and program (in German)
...
CSC News:
Melina Freitag visiting
May 2nd, 2011
Melina Freitag (University of Bath) will be visiting us in the first week of May (02-06). Melina is an expert on eigenvalue problems and their numerical solution with a particular focus on preconditioned inverse iteration. She has also worked extensively on inverse problems in weather forecasting in collaboration with the Met Office. Melina gives an seminar talk on
Preconditioned inverse iteration and shift-invert Arnoldi method (05/03/11, 15:00).
CSC News:
Jens in Osijek, Croatia
May 2nd, 2011
Jens Saak is invited to J. J. Strossmayer University of Osijek to give a lecture on Algebraic Riccati Equations from May 2 to 06. Additionally he give a colloquiums talk at 5th May on Numerical Solution of Linear Quadratic Regulator Problems under PDE Constraints.
CSC News:
4 Contributed Talks at GAMM Annual Meeting in Graz
April 18th, 2011
Tobias Breiten, Patrick Kürschner, Thomas Mach and Matthias Voigt give contributed talks at the GAMM Annual Meeting 2011 at TU Graz.
April 11th, 2011
Hermann Mena (ENP Quito, Ecuador) is visiting the MPI Magdeburg again for two weeks.
CSC News:
First CSC research group weekend workshop
April 7th, 2011
CSC research group met the first time for a research group weekend workshop in
Clausthal Zellerfeld in the Harz Mountains from April 7th to April 11th. Besides 14 discussion forums about problems of the recent group research a visit in a local
glass factory, a BBQ, a hike, a campfire, and sports (
Bildungsstätte der Sportjugend Niedersachsen) was scheduled.
March 21st, 2011
Timo Reis from
TU Berlin/TU Hamburg-Harburg is visiting CSC in the period from March 21st to March 25th. Reason for his visit is ongoing work in the area of model order reduction together with André Schneider. He will give a
CSC seminar talk about
Infinite-Dimensional Systems and Balanced Truncation on March 23th, 10:00 (V1.06).
February 11th, 2011
The preconditioned inverse iteration is an efficient method to compute the smallest eigenpair of a symmetric positive definite matrix ℋ. Here we use this method to find the smallest eigenvalues of a hierarchical matrix. We use ℋ-arithmetic to precondition with an approximate inverse of M or an approximate Cholesky decomposition of M. In general ℋ-arithmetic is of linear-polylogarithmic complexity, so the computation of one eigenvalue is cheap.
We extend the ideas to the computation of inner eigenvalues by computing an invariant subspaces S of (M-\mu I)² by subspace preconditioned inverse iteration.
February 3rd, 2011
The Otto von Guericke University Magdeburg has recently announced that they have granted Peter Benner the title of Honorary Professor in Mathematics. Press release (in German)
...
January 25th, 2011
Hermann Mena (ENP Quito, Ecuador) is visiting the MPI Magdeburg again. Together with
René Schneider (TU Chemitz) we will continue the cooperation in the project
aerial-spray-drift.
January 20th, 2011
Group member Judith Schneider (sub project 3 within the MoreSim4Nano research network) and André Bodendiek (sp 1,
TU Braunschweig) visit partners of sp 2 at
TU Darmstadt on 3rd of February. Furthermore, the
new project webpages are available now.
January 20th, 2011
Peter Benner, Martin Heß, Jens Saak, Judith Schneider und André Schneider join the
Workshop on Model Order Reduction in Optimization and Control with PDEs from 26th to 28th January 2011 at
WIAS in Berlin.
January 3rd, 2011
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.
Events:
Verteidigung Diplomarbeit
December 21st, 2010
Am 21. Dezember 2010, 14:00 Uhr, verteidigt Heiko Weichelt seine Diplomarbeit mit dem Titel Feedback-Stabilisierung von instationären, inkompressiblen Strömungen mit Riccati-Ansatz in Chemnitz im Raum 2/B202.
Events:
Verteidigung Diplomarbeit
December 15th, 2010
Am 15. Dezember 2010, 16:00 Uhr, verteidigt Martin Köhler seine Diplomarbeit mit dem Titel H_{2} Modellreduktion Verfahren-Implementierung-Vergleich in Chemnitz im Raum 2/41/638.
November 17th, 2010
We use a bisection method to compute the eigenvalues of a symmetric ℋ_{ℓ}-matrix M. The bisection method requires matrix-size independent many iterations to find an eigenvalue up to the desired accuracy, so that an eigenvalue can be found in linear-polylogarithmic time. Numerical experiments demonstrate the efficiency of the algorithm, in particular for the case where some interior eigenvalues are required.
CSC News:
New CSC Webpage
November 16th, 2010
The new Group Webpage is almost complete. We have copied large parts of the old
MiIT-Webpage, neverless some parts are still under construction. If you do not find the informations you search, do not hesitate to ask us!
November 5th, 2010
The colloquium is dedicated to our new director Prof. Peter Benner. We continue the colloquium on Friday with mathematical talks presenting selected topics of Peter Benner's research group.
September 1st, 2010
As of September 1, 2010, Peter Benner has taken up his position as a director at the
Max-Planck-Institute for Dynamics of Complex Technical Systems in Magdeburg full-time. At MPI Magdeburg, he leads the group
Computational Methods in Systems and Control Theory (CSC). Additionally, he will also keep the
"Mathematics in Industry and Technology" professorship in Chemnitz on an extraofficial basis.
Most of the MiIT group has moved to Magdeburg, too.
Thesis Topic:
Diplom/Master Thesis
Development and implementation of a Multigrid-ADI method for solving Lyapunov equations
Thesis Topic:
Diplom/Master Thesis
Computation of Lyapunov exponents for dynamical systems
Thesis Topic:
Diplom/Master Thesis
Development and comparison of model reduction methods for concrete applications (several topics, possibility to work in a group)