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- Title
Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey.
- Authors
Benner, Peter; Saak, Jens
- Abstract
Efficient numerical algorithms for the solution of large and sparse matrix Riccati and Lyapunov equations based on the low rank alternating directions implicit (ADI) iteration have become available around the year 2000. Over the decade that passed since then, additional methods based on extended and rational Krylov subspace projection have entered the field and proved to be competitive alternatives. In this survey we sketch both types of methods and discuss their advantages and drawbacks. We focus on the continuous time case here, but corresponding results for discrete time problems can for most results be found in the available literature. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
- Subjects
SPARSE matrices; RICCATI equation; LYAPUNOV functions; KRYLOV subspace; NUMERICAL analysis
- Publication
GAMM Mitteilungen, 2013, Vol 36, Issue 1, p32
- ISSN
0936-7195
- Publication type
Article
- DOI
10.1002/gamm.201310003