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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Vydáno v:SIAM journal on matrix analysis and applications Ročník 28; číslo 4; s. 1097 - 1125
Hlavní autor: Grubis ic, Luka
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2006
Témata:
Approximation
Eigenvalues
Eigenvectors
Estimates
Hilbert space
ISSN:0895-4798, 1095-7162
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0895-4798
1095-7162
DOI:10.1137/050626533