Benner, PeterBreiten, TobiasMax-Planck-Institut für Dynamik Komplexer Technischer Systeme2025-05-292012https://epflicht.bibliothek.uni-halle.de/handle/123456789/3863870253808urn:nbn:de:gbv:3:2-638722480403Abstract: 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.1 Online-Ressource (32 Seiten = 0,45 MB) : Diagrammeenghttp://rightsstatements.org/vocab/InC/1.0/510Book