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Computing inner eigenvalues of matrices in tensor train matrix format / Thomas Mach
VerfasserMach, Thomas
KörperschaftMax-Planck-Institut für Dynamik Komplexer Technischer Systeme
ErschienenMagdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, December 5, 2011
Umfang1 Online-Ressource (11 Seiten = 0,12 MB) : Diagramm
SpracheEnglisch
SerieMax Planck Institute Magdeburg Preprints ; 11-09
URNurn:nbn:de:gbv:3:2-63868 
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Computing inner eigenvalues of matrices in tensor train matrix format [0.12 mb]
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Abstract: The computation of eigenvalues is one of the core topics of numerical mathematics. We will discuss an eigenvalue algorithm for the computation of inner eigenvalues of a large symmetric and positive definite matrix M based on the preconditioned inverse iteration xi+1 = xi - B-1 (Mxi - μ(xi) xi) and the folded spectrum method (replace M by (M-σI)²). We assume that M is given in the tensor train matrix format and use the TT-toolbox from I.V. Oseledets (see http://spring.inm.ras.ru/osel/) for the numerical computations. We will present first numerical results and discuss the numerical difficulties. A shorted version of this preprint was submitted to the Proceedings of the ENUMATH 2011 (Leicester).