Team Leader NLMA

Prof. Dr. Peter Benner
Prof. Dr. Peter Benner
Phone: +49 391 6110 450
Fax: +49 391 6110 453
Room: S2.15

Team members

Dr. Pawan Goyal
Dr. Pawan Goyal
Phone: +49 391 6110 386
Room: S3.09
Dr. Patrick Kürschner
Dr. Patrick Kürschner
Phone: +49 391 6110 424
Room: S2.14
Dr. Akwum Onwunta
Dr. Akwum Onwunta
Phone: +49 391 6110 808
Room: S1.05
Carolin Penke, M.Sc.
Carolin Penke, M.Sc.
Phone: +49 391 6110 806
Room: S3.09
Roman Weinhandl
Phone: +49 391 6110 472
Room: S2.14
Kirandeep Kour
Phone: +49 391 6110 345
Room: S1.05
Dr. Jens Saak
Dr. Jens Saak
Phone: +49 391 6110 216
Fax: +49 391 6110 453
Room: S2.20
Dr. Yue Qiu
Dr. Yue Qiu
Phone: +49 391 6110 395
Room: S3.13
Dipl.-Math. Martin Köhler
Dipl.-Math. Martin Köhler
Phone: +49 391 6110 445
Fax: +49 391 6110 453
Room: S3.10
Cleophas Kweyu
Cleophas Kweyu
Phone: +49 391 6110 464
Room: S2.09

Numerical Linear and Multilinear Algebra

Numerical Linear and Multilinear Algebra

We study numerical methods for linear and nonlinear eigenvalue problems. This includes the development and analysis of new algorithms, (backward) error analysis, and the derivation of the associated (relative) perturbation theory.  Special attention is given to linear, generalized, and polynomial eigenproblems with spectral symmetries. Special cases include:
  • linear eigenproblems for Hamiltonian and symplectic matrices,
  • generalized eigenproblems for skew-Hamiltonian/Hamiltonian, even, and positive definite matrix pencils,
  • as well as even, gyroscopic, and hyperbolic polynomial eigenvalue problems.
Such problems often arise in systems, control and stability theory, FE analysis of corner singularities, discrete approximations to the Schrödinger equation such as the Hartree-Fock and Bethe-Salpeter equations, and many other areas. Another important class of structured eigenproblems investigated by the NLMA team is related to rank-structured matrices and matrix pairs. This includes H- and H2-matrices resulting from FEM and BEM discretizations of PDE eigenvalue problems, but also matricizations of tensor equations in electronic structure calculation.    

Moreover, we investigate the solution of special linear systems of equations arising in PDE control and model reduction algorithms. This includes in particular
  • recycling techniques for Krylov subspace solvers for systems with multiple-right hand sides and constant (or slowly varying) coefficient matrices,
  • preconditioning techniqes for saddle point problems, and
  • using tensor techniques to solve high-dimensional problems like stochastic Galerkin systems. 

 

Projects

Structured (Hamiltonian, even) eigenvalue problems
Partners: Zvonimir Bujanović (U Zagreb), Heike Faßbender (TU Braunschweig), Volker Mehrmann, Matthias Voigt (TU Berlin), Hongguo Xu (U Kansas, Lawrence, KS), Chao Yang (LLBL Berkeley, CA)Funded by: MPIFunding period:  Contact: Peter Benner

Structured (Hamiltonian, even) eigenvalue problems

Partners: Zvonimir Bujanović (U Zagreb), Heike Faßbender (TU Braunschweig), Volker Mehrmann, Matthias Voigt (TU Berlin), Hongguo Xu (U Kansas, Lawrence, KS), Chao Yang (LLBL Berkeley, CA)
Funded by: MPI
Funding period:
Contact: Peter Benner

Efficient Solvers for the Bethe-Salpeter Equations
Partners: MPCDF, Claudia Draxl (HU Berlin, Physik), Chao Yang (LBL), Heike Faßbender (TU Braunschweig), Boris Khoromskii, Venera Khoromskaia (MPI for Mathematics in the Sciences, Leipzig).Funded by: MPI, co-financed by MPI MIS, Leipzig and MPCDF Funding period: MPI, MPI MIS (2018-2020) and MPCDF (2017-2020)Contact: Prof. Peter Benner, Dr. Venera Khoromskaia 
 

Efficient Solvers for the Bethe-Salpeter Equations

Partners: MPCDF, Claudia Draxl (HU Berlin, Physik), Chao Yang (LBL), Heike Faßbender (TU Braunschweig), Boris Khoromskii, Venera Khoromskaia (MPI for Mathematics in the Sciences, Leipzig).
Funded by: MPI, co-financed by MPI MIS, Leipzig and MPCDF
Funding period: MPI, MPI MIS (2018-2020) and MPCDF (2017-2020)
Contact: Prof. Peter Benner, Dr. Venera Khoromskaia
 
Tensor techniques for high-dimensional linear systems
Partners:Martin Stoll (TU Chemintz), Sergey Dolgov (Bath university, UK) Funded by:CDS, IMPRS Funding period:   Contact: Peter Benner, Akwum Onwunta

Tensor techniques for high-dimensional linear systems

Partners:Martin Stoll (TU Chemintz), Sergey Dolgov (Bath university, UK)
Funded by:CDS, IMPRS
Funding period:
Contact: Peter Benner, Akwum Onwunta

Concluded Projects

Numerical methods of nonlinear eigenvalue problems
Partner: Ninoslav Truhar, Suzana Miodragović (J.J. Strossmayer Univerity Osijek)  funded by: DAAD PPP (Croatia)  Funding period:   Contact: Peter Benner, Xin Liang

Numerical methods of nonlinear eigenvalue problems

Partner: Ninoslav Truhar, Suzana Miodragović (J.J. Strossmayer Univerity Osijek)
funded by: DAAD PPP (Croatia)
Funding period:
Contact: Peter Benner, Xin Liang

 
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