Team Leader ME

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

Team Members

Dr. Jan Heiland
Dr. Jan Heiland
Phone: +49 391 6110 476
Björn Baran
Björn Baran
Phone: +49 391 6110 413
Manuela Hund
Manuela Hund
Phone: +49 391 6110 492
Links: ORCID
Dipl.-Math. Martin Köhler
Dipl.-Math. Martin Köhler
Phone: +49 391 6110 445
Fax: +49 391 6110 453
Steffen Werner, M.Sc.
Steffen Werner, M.Sc.
Phone: +49 391 6110 484
Links: ORCID

Research Assistants

Currently none

Matrix Equations

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.

Current Projects

Project Scientists Funded by Partners
Improved and Structure-Aware Solvers for Large-Scale Algebraic Matrix Equations Benner, Saak, Kürschner, Weichelt, Bujanović, Breiten, Uddin

MPI
DFG SPP1253 (until 10/2013)

Uni Augsburg (Stykel), UJI Castellón (Quintana-Ortí)
Indefinite Factorization Based Solvers for Large-Scale Differential Matrix Equations and Applications Saak, Lang (TU Chemnitz) MPI Uni Augsburg (Stykel), Uni Innsbruck (Mena)
High Performance Solvers for Dense Differential and Algebraic Matrix Equations Saak, Köhler, Benner, Lang (TU Chemnitz) MPI UJI Castellón (Quintana-Ortí), Uni de la República Montevideo (Ezzatti)
Solving Parametric Sylvester Equations for Model Order Reduction Saak, Hund MPI

Concluded Projects

Project Scientists Funded by Partners
Linear plus Positive Equations with Applications in Bilinear and Stochastic Control Benner, Breiten, Redmann MPI TU Kaiserslautern (Damm)
Mathematical Software for Dense Matrix Equations (SLICOT) Benner, Voigt, Köhler, Saak Niconet e.V.,
MPI
National Institute for Research & Development in Informatics, Bucharest (Sima)
 
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