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dc.contributor.authorKandler, Ute
dc.contributor.authorChristian, Schröder
dc.description.abstractWe investigate the convergence behavior of inexact Krylov methods for the approximation of a few eigenvectors or invariant subspaces of a large, sparse Hermitian matrix. Bounds on the distance between an exact invariant subspace and a Krylov subspace and between an exact invariant subspace and a Ritz space are presented. Using the first bound we analyze the question: if a few iteration steps have been taken without convergence, how many more iterations have to be performed to achieve a preset tolerance. The second bound provides a measure on the approximation quality of a computed Ritz space. Traditional bounds of these quantities are particularly sensitive to the gap between the wanted eigenvalues and the remaining spectrum. Here this gap is allowed to be small by considering how well the exact invariant subspace is contained in a slightly larger approximated invariant subspace. Moreover, numerical experiments confirm the applicability of the given bounds.en
dc.subject.ddc510 Mathematiken
dc.subject.otherHermitian eigenvalue problemen
dc.subject.otherinexact Krylov methoden
dc.subject.otherconvergence analysisen
dc.subject.otherKrylov relationen
dc.subject.otherRitz pairen
dc.titleSpectral error bounds for Hermitian inexact Krylov methodsen
dc.typeResearch Paperen
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2014, 11en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften » Inst. Mathematikde
tub.subject.msc200065F15 Eigenvalues, eigenvectorsen
tub.subject.msc200065G99 None of the above, but in this sectionen
Appears in Collections:Technische Universität Berlin » Publications

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