Low rank methods for a class of generalized Lyapunov equations and related issues / Peter Benner, Tobias Breiten
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Low rank methods for a class of generalized Lyapunov equations and related issues
Discovery
870318772
URN
urn:nbn:de:gbv:3:2-63947
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Publication history
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, February 21, 2012
Content
1 Online-Ressource (25 Seiten = 0,44 MB) : Diagramme
Edition
Language
eng
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Abstract
Abstract: In this paper, we study possible low rank solution methods for generalized Lyapunov equations arising in bilinear and stochastic control. We show that under certain assumptions one can expect a strong singular value decay in the solution matrix allowing for low rank approximations. Since the theoretical tools strongly make use of a connection to the standard linear Lyapunov equation, we can even extend the result to the d-dimensional case described by a tensorized linear system of equations. We further provide some reasonable extensions of some of the most frequently used linear low rank solution techniques such as the alternating directions implicit (ADI) iteration and the Krlyov-plus-inverse-Krylov (KPIK) method. By means of some standard numerical examples used in the area of bilinear model order reduction, we will show the efficiency of the new methods.
Series
Max Planck Institute Magdeburg Preprints ; 12-03 ppn:870173030