On Eigenvalue and Eigenvector Estimates for Nonnegative Definite Operators

We present a perturbation approach to the Rayleigh-Ritz approximations in the sense of Davis, Kahan, and Weinberger. We restrict ourselves to nonnegative definite self-adjoint operators and obtain sharp bounds of relative type for both eigenvalues and eigenvectors. The operators are allowed to have...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications Vol. 28; no. 4; pp. 1097 - 1125
Main Author: Grubis ic, Luka
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2006
Subjects:
Approximation
Eigenvalues
Eigenvectors
Estimates
Hilbert space
ISSN:0895-4798, 1095-7162
Online Access:Get full text
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Summary:We present a perturbation approach to the Rayleigh-Ritz approximations in the sense of Davis, Kahan, and Weinberger. We restrict ourselves to nonnegative definite self-adjoint operators and obtain sharp bounds of relative type for both eigenvalues and eigenvectors. The operators are allowed to have nontrivial null-spaces, and the test spaces need not be contained in the domain of the considered operator.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0895-4798
1095-7162
DOI:10.1137/050626533