Convergence theory of exact interpolation scheme for computing several eigenvectors

Summary An asymptotic convergence analysis of a new multilevel method for numerical solution of eigenvalues and eigenvectors of symmetric and positive definite matrices is performed. The analyzed method is a generalization of the original method that has recently been proposed by R. Kužel and P. Van...

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Vydáno v:Numerical linear algebra with applications Ročník 23; číslo 2; s. 373 - 390
Hlavní autor: Pultarova, I
Médium: Journal Article
Jazyk:angličtina
Vydáno: Oxford Blackwell Publishing Ltd 01.03.2016
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Témata:
Approximation
Asymptotic properties
Convergence
convergence rate
Eigenvectors
Interpolation
Mathematical analysis
Mathematical models
Multilevel
multilevel methods
numerical computation of eigenvalues and eigenvectors
Rayleigh quotient
ISSN:1070-5325, 1099-1506
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Shrnutí:Summary An asymptotic convergence analysis of a new multilevel method for numerical solution of eigenvalues and eigenvectors of symmetric and positive definite matrices is performed. The analyzed method is a generalization of the original method that has recently been proposed by R. Kužel and P. Vaněk (DOI: 10.1002/nla.1975) and uses a standard multigrid prolongator matrix enriched by one full column vector, which approximates the first eigenvector. The new generalized eigensolver is designed to compute m≥1 eigenvectors. Their asymptotic convergence in terms of the generalized residuals is proved, and its convergence factor is estimated. The theoretical analysis is illustrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.
Bibliografie:ArticleID:NLA2029
Faculty of Mathematics and Physics
ark:/67375/WNG-2MK5XLKG-6
Charles University in Prague
istex:D8963CDC1E8FEDFA56EF5E6025088AE643F33BAB
ERC-CZ - No. LL1202
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1070-5325
1099-1506
DOI:10.1002/nla.2029