On best approximations of polynomials in matrices in the matrix 2-norm
| dc.contributor.author | Liesen, Jörg | |
| dc.contributor.author | Tichý, Petr | |
| dc.date.accessioned | 2017-12-19T15:20:18Z | |
| dc.date.available | 2017-12-19T15:20:18Z | |
| dc.date.issued | 2009-07-30 | |
| dc.description.abstract | We 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.eissn | 1095-7162 | |
| dc.identifier.issn | 0895-4798 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/7286 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-6559 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 515 Analysis | de |
| dc.subject.ddc | 512 Algebra | de |
| dc.subject.other | matrix approximation problems | en |
| dc.subject.other | polynomials in matrices | en |
| dc.subject.other | matrix functions | en |
| dc.subject.other | matrix 2-norm | en |
| dc.subject.other | GMRES | en |
| dc.subject.other | Arnoldi’s method | en |
| dc.title | On best approximations of polynomials in matrices in the matrix 2-norm | en |
| dc.type | Article | en |
| dc.type.version | publishedVersion | en |
| dcterms.bibliographicCitation.doi | 10.1137/080728299 | en |
| dcterms.bibliographicCitation.issue | 2 | en |
| dcterms.bibliographicCitation.journaltitle | SIAM Journal on Matrix Analysis and Applications | en |
| dcterms.bibliographicCitation.originalpublishername | Society for Industrial and Applied Mathematics | en |
| dcterms.bibliographicCitation.originalpublisherplace | Philadelphia, Pa | en |
| dcterms.bibliographicCitation.pageend | 863 | en |
| dcterms.bibliographicCitation.pagestart | 853 | en |
| dcterms.bibliographicCitation.volume | 31 | en |
| tub.accessrights.dnb | domain | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Numerische Lineare Algebra | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.group | FG Numerische Lineare Algebra | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |