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 in | Numerical linear algebra with applications Vol. 22; no. 2; pp. 220 - 232 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Oxford
Blackwell Publishing Ltd
01.03.2015
Wiley Subscription Services, Inc |
Subjects | |
Online Access | Get full text |
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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. |
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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 |