A new framework for implicit restarting of the Krylov-Schur algorithm

SummaryThis paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank‐one correction, implemented using only the eleme...

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Published inNumerical linear algebra with applications Vol. 22; no. 2; pp. 220 - 232
Main Authors Bujanovic, Zvonimir, Drmac, Zlatko
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.03.2015
Wiley Subscription Services, Inc
Subjects
Algorithms
Arnoldi algorithm
eigenvalue assignment
Eigenvalues
implicit restart
Krylov-Schur algorithm
Linear algebra
Online
polynomial filter
Polynomials
QR algorithm
Rayleigh quotient
Restarting
Ritz values
Similarity
Transformations (mathematics)
Translations
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Summary:SummaryThis paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank‐one correction, implemented using only the elementary transformations (translation and similarity) of the Krylov decomposition. This framework includes the implicitly restarted Arnoldi (IRA) algorithm and the Krylov–Schur algorithm with implicit harmonic restart as special cases. Further, it reveals that the IRA algorithm can be turned into an eigenvalue assignment method. Copyright © 2014 John Wiley & Sons, Ltd.
Bibliography:istex:3D23C6A01D66C591191A0BB9256C4653C0CF4B33
ArticleID:NLA1944
ark:/67375/WNG-SS94DG0N-1
On leave from Department of Mathematics, University of Zagreb
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1070-5325
1099-1506
DOI:10.1002/nla.1944