On best approximations of polynomials in matrices in the matrix 2-norm

dc.contributor.authorLiesen, Jörg
dc.contributor.authorTichý, Petr
dc.date.accessioned2017-12-19T15:20:18Z
dc.date.available2017-12-19T15:20:18Z
dc.date.issued2009-07-30
dc.description.abstractWe show that certain matrix approximation problems in the matrix 2-norm have uniquely defined solutions, despite the lack of strict convexity of the matrix 2-norm. The problems we consider are generalizations of the ideal Arnoldi and ideal GMRES approximation problems introduced by Greenbaum and Trefethen [SIAM J. Sci. Comput., 15 (1994), pp. 359–368]. We also discuss general characterizations of best approximation in the matrix 2-norm and provide an example showing that a known sufficient condition for uniqueness in these characterizations is not necessary.en
dc.identifier.eissn1095-7162
dc.identifier.issn0895-4798
dc.identifier.urihttps://depositonce.tu-berlin.de//handle/11303/7286
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-6559
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc515 Analysisde
dc.subject.ddc512 Algebrade
dc.subject.othermatrix approximation problemsen
dc.subject.otherpolynomials in matricesen
dc.subject.othermatrix functionsen
dc.subject.othermatrix 2-normen
dc.subject.otherGMRESen
dc.subject.otherArnoldi’s methoden
dc.titleOn best approximations of polynomials in matrices in the matrix 2-normen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.1137/080728299en
dcterms.bibliographicCitation.issue2en
dcterms.bibliographicCitation.journaltitleSIAM Journal on Matrix Analysis and Applicationsen
dcterms.bibliographicCitation.originalpublishernameSociety for Industrial and Applied Mathematicsen
dcterms.bibliographicCitation.originalpublisherplacePhiladelphia, Paen
dcterms.bibliographicCitation.pageend863en
dcterms.bibliographicCitation.pagestart853en
dcterms.bibliographicCitation.volume31en
tub.accessrights.dnbdomainen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematik>FG Numerische Lineare Algebrade
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Numerische Lineare Algebrade
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
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