Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations : a state of the art survey / Peter Benner, Jens Saak
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Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations
Discovery
870436449
URN
urn:nbn:de:gbv:3:2-64200
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Publication history
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, June 24, 2013
Content
1 Online-Ressource (23 Seiten = 0,36 MB)
Edition
Language
eng
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Abstract
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 and will be referred to throughout the paper.
Series
Max Planck Institute Magdeburg Preprints ; 13-07 ppn:870173030