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Rational interpolation methods for symmetric Sylvester equations / Peter Benner, Tobias Breiten
VerfasserBreiten, Tobias ; Benner, Peter
KörperschaftMax-Planck-Institut für Dynamik Komplexer Technischer Systeme
ErschienenMagdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, December 10, 2013
Umfang1 Online-Ressource (19 Seiten = 0,8 MB) : Illustrationen
SpracheEnglisch
SerieMax Planck Institute Magdeburg Preprints ; 13-23
URNurn:nbn:de:gbv:3:2-64381 
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Rational interpolation methods for symmetric Sylvester equations [0.8 mb]
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Abstract: We discuss low rank approximation methods for large-scale symmetric Sylvester equations. Following similar discussions for the Lyapunov case we introduce an energy norm by the symmetric Sylvester operator. Given a rank nr we derive necessary conditions for an approximation being optimal with respect to this norm. We show that the norm minimization problem is related to an objective function based on the H2-inner product for symmetric state space systems. This objective function is shown to exhibit first-order conditions that are equivalent to the ones from the norm minimization problem. We further propose an iterative procedure and demonstrate its efficiency when used within image reconstruction problems.