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Titel
Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations : a state of the art survey / Peter Benner, Jens Saak
VerfasserBenner, Peter ; Saak, Jens
KörperschaftMax-Planck-Institut für Dynamik Komplexer Technischer Systeme
ErschienenMagdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, June 24, 2013
Umfang1 Online-Ressource (23 Seiten = 0,36 MB)
SpracheEnglisch
SerieMax Planck Institute Magdeburg Preprints ; 13-07
URNurn:nbn:de:gbv:3:2-64200 
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Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations [0.36 mb]
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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.