Team Leader ME

Dr. Jens Saak
Dr. Jens Saak
Phone: +49 391 6110 216
Fax: +49 391 6110 453
Room: S2.20

Team Members

Dr. Jan Heiland
Dr. Jan Heiland
Phone: +49 391 6110 476
Room: S2.13
Dr. Patrick Kürschner
Dr. Patrick Kürschner
Phone: +49 391 6110 424
Room: S2.14
Dr. Tony Stillfjord
Dr. Tony Stillfjord
Phone: +49 391 6110 377
Room: S3.14
Björn Baran
Björn Baran
Phone: +49 391 6110 413
Room: S3.14
Manuela Hund
Manuela Hund
Phone: +49 391 6110 492
Room: S2.09
Links: ORCID
Dipl.-Math. Martin Köhler
Dipl.-Math. Martin Köhler
Phone: +49 391 6110 445
Fax: +49 391 6110 453
Room: S3.10
Steffen Werner, M.Sc.
Steffen Werner, M.Sc.
Phone: +49 391 6110 484
Room: S2.09
Links: ORCID

Research Assistants

Currently none

Matrix Equations

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Matrix Equations

Matrix equations of the one kind or the other are a central tool in all kinds of applications. In optimal control the linear quadratic control problem features a feedback solution that is determined via the solution of an algebraic Riccati equation. The system Gramians of a linear time invariant dynamical system are the solutions of two adjoint Lyapunov equations. Riccati, Lyapunov and Sylvester equations play an important role in different model order reduction techniques for continuous time linear dynamical systems. They all have discrete time counterparts as e.g. the well known Stein equations. Krylov subspace and eigenvalue methods can be related to certain Sylvester equations, as well.
Nearly all other research field of the CSC group involve matrix equation computations at a certain point. The work of this team is dedicated to the efficient numerical solution of the variety of those equations in all kinds of working environments.

Internal Projects

Partner: Uni Augsburg, UJI Castellón, Uni Zagreb, FAU Erlangen, Uni Bath
funded by: MPI, DFG SPP1253 (until 10/2013), EU-MORNET (2/2018 - 3/2018)
Funding Period: seit 10/2010
Contact: Peter Benner, Jens Saak, Patrick Kürschner

Improved and Structure-Aware Solvers for Large-Scale Algebraic Matrix Equations

Partner: Uni Augsburg, UJI Castellón, Uni Zagreb, FAU Erlangen, Uni Bath
funded by: MPI, DFG SPP1253 (until 10/2013), EU-MORNET (2/2018 - 3/2018)
Funding Period: seit 10/2010
Contact: Peter Benner, Jens Saak, Patrick Kürschner

Indefinite Factorization Based Solvers for Large-Scale Differential Matrix Equations and Applications

Partner: Uni Augsburg, Yachay Tech
funded by: MPI
Funding Period: since 10/2010
Contact: Peter Benner, Jens Saak, Norman Lang (TU Chemnitz), Björn Baran

Splitting methods for large-scale nonlinear differential matrix equations

Partner: tba
funded by: MPI
Funding Period: since 09/2017
Contact: Tony Stillfjord

Projection-based solvers for differential matrix equations

funded by: MPI
Funding Period: since
Contact: Jan Heiland, Maximilian Behr

High Performance Solvers for Dense Differential and Algebraic Matrix Equations

Partner: TU Dresden, UJI Castellón, UdelaR Montevideo
funded by: MPI
Funding Period: since 01/2011
Contact: Jens Saak, Martin Köhler
Partner: Uni Bath, Uni Washington
funded by: MPI
Funding Period: since 10/2014
Contact: Patrick Kürschner

Multiterm Sylvester-type equation solvers

Partner: Uni Bath, Uni Washington
funded by: MPI
Funding Period: since 10/2014
Contact: Patrick Kürschner

Solving Parametric Sylvester Equations for Model Order Reduction

funded by: MPI
Funding Period: since 06/2014
Contact: Jens Saak, Manuela Hund

Concluded Projects

Linear plus Positive Equations with Applications in Bilinear and Stochastic Control

Partner: TU Kaiserslautern
funded by:
MPI
Contact: Peter Benner

Mathematical Software for Dense Matrix Equations (SLICOT)

Partner: National Institute for Research & Development in Informatics, Bucharest
funded by: Niconet e.V., MPI
Contact: Peter Benner, Jens Saak, Martin Köhler
 
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