Handle URI:
http://hdl.handle.net/10754/599675
Title:
Some observations on weighted GMRES
Authors:
Güttel, Stefan; Pestana, Jennifer
Abstract:
We investigate the convergence of the weighted GMRES method for solving linear systems. Two different weighting variants are compared with unweighted GMRES for three model problems, giving a phenomenological explanation of cases where weighting improves convergence, and a case where weighting has no effect on the convergence. We also present a new alternative implementation of the weighted Arnoldi algorithm which under known circumstances will be favourable in terms of computational complexity. These implementations of weighted GMRES are compared for a large number of examples. We find that weighted GMRES may outperform unweighted GMRES for some problems, but more often this method is not competitive with other Krylov subspace methods like GMRES with deflated restarting or BICGSTAB, in particular when a preconditioner is used. © 2014 Springer Science+Business Media New York.
Citation:
Güttel S, Pestana J (2014) Some observations on weighted GMRES. Numerical Algorithms 67: 733–752. Available: http://dx.doi.org/10.1007/s11075-013-9820-x.
Publisher:
Springer Nature
Journal:
Numerical Algorithms
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
10-Jan-2014
DOI:
10.1007/s11075-013-9820-x
Type:
Article
ISSN:
1017-1398; 1572-9265
Sponsors:
S.G. was supported by Deutsche Forschungsgemeinschaft Fellowship No. GU 1244/1-1. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorGüttel, Stefanen
dc.contributor.authorPestana, Jenniferen
dc.date.accessioned2016-02-28T06:07:16Zen
dc.date.available2016-02-28T06:07:16Zen
dc.date.issued2014-01-10en
dc.identifier.citationGüttel S, Pestana J (2014) Some observations on weighted GMRES. Numerical Algorithms 67: 733–752. Available: http://dx.doi.org/10.1007/s11075-013-9820-x.en
dc.identifier.issn1017-1398en
dc.identifier.issn1572-9265en
dc.identifier.doi10.1007/s11075-013-9820-xen
dc.identifier.urihttp://hdl.handle.net/10754/599675en
dc.description.abstractWe investigate the convergence of the weighted GMRES method for solving linear systems. Two different weighting variants are compared with unweighted GMRES for three model problems, giving a phenomenological explanation of cases where weighting improves convergence, and a case where weighting has no effect on the convergence. We also present a new alternative implementation of the weighted Arnoldi algorithm which under known circumstances will be favourable in terms of computational complexity. These implementations of weighted GMRES are compared for a large number of examples. We find that weighted GMRES may outperform unweighted GMRES for some problems, but more often this method is not competitive with other Krylov subspace methods like GMRES with deflated restarting or BICGSTAB, in particular when a preconditioner is used. © 2014 Springer Science+Business Media New York.en
dc.description.sponsorshipS.G. was supported by Deutsche Forschungsgemeinschaft Fellowship No. GU 1244/1-1. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Natureen
dc.subjectHarmonic Ritz valuesen
dc.subjectKrylov subspace methoden
dc.subjectLinear systemsen
dc.subjectWeighted GMRESen
dc.titleSome observations on weighted GMRESen
dc.typeArticleen
dc.identifier.journalNumerical Algorithmsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversity of Manchester, Manchester, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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