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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices
Lars Grasedyck, Wolfgang Hackbusch and Boris N. KhoromskijAbstract
In previous papers, a class of hierarchical matrices (H-matrices) is introduced which are data-sparse and allow an approximate matrix arithmetic of almost optimal complexity. Here, we investigate a new approach to exploit the H-matrix structure for the solution of large scale Lyapunov and Riccati equations as they typically arise for optimal control problems where the constraint is a partial differential equation of elliptic type. This approach leads to an algorithm of linear-logarithmic complexity in the size of the matrices.
- Received:
- 30.07.02
- Published:
- 30.07.02
- MSC Codes:
- 65F05, 65F30, 65F50
- Keywords:
- hierarchical matrices, riccati equation, lyapunov equation