21st GAMM-Seminar Leipzig on
Robust Fast Solvers

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  21st GAMM-Seminar
January, 26th-28th, 2005
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  Abstract Lars Grasedyck, Wed, 15.30-16.00 Previous Contents Next  
  A Multigrid Method to Solve Large Scale Sylvester Equations
Lars Grasedyck (MPI Leipzig)

(joint work with Wolfgang Hackbusch)

The talk is subdivided into three parts. In the first part we give a brief and incomplete overview of the existing methods for the solution of large scale matrix equations, namely Lyapunov, Sylvester and Riccati equations. In the second part the framework for multigrid methods (geometric and algebraic) for Sylvester equations is introduced. These allow to compute the N by N solution matrix in O(N2). In the last part we consider a framework that preserves a given low-rank structure in the right-hand side as it is naturally given in the context of model reduction. For N by N matrices we can compute the N by N solution matrix in O(N log2 N) complexity. The talk closes with some numerical examples.


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Last updated:
28.01.2005 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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