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Titel
On optimality of interpolation-based low rank approximations of large-scale matrix equations / Peter Benner, Tobias Breiten
VerfasserBenner, Peter ; Breiten, Tobias
KörperschaftMax-Planck-Institut für Dynamik Komplexer Technischer Systeme
ErschienenMagdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, February 3, 2012
Umfang1 Online-Ressource (32 Seiten = 0,45 MB) : Diagramme
SpracheEnglisch
SerieMax Planck Institute Magdeburg Preprints ; 11-10
URNurn:nbn:de:gbv:3:2-63872 
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On optimality of interpolation-based low rank approximations of large-scale matrix equations [0.45 mb]
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Abstract: In this paper, we will discuss some optimality results for the approximation of large-scale matrix equations. In particular, this will include the special case of Lyapunov and Sylvester equations, respectively. We show a relation between the iterative rational Krylov algorithm and a Riemannian optimization method which recently has been shown to locally minimize a certain energy norm of the underlying Lyapunov operator. Moreover, we extend the results for a more general setting leading to a slight modification of IRKA. By means of some numerical test examples, we will show the efficiency of the proposed methods.

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Abstract: In this paper we will discuss some optimality results for the approximation of large-scale matrix equations. In particular this will include the special case of Lyapunov and Sylvester equations respectively. We show a relation between the iterative rational Krylov algorithm and a Riemannian optimization method which recently has been shown to locally minimize a certain energy norm of the underlying Lyapunov operator. Moreover we extend the results for a more general setting leading to a slight modification of IRKA. By means of some numerical test examples we will show the efficiency of the proposed methods.