Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.1082
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dc.contributor.authorPaige, Christopher C.-
dc.contributor.authorPanayotov, Ivo-
dc.contributor.authorZemke, Jens-Peter M.-
dc.date.accessioned2012-12-17T08:35:20Zde_DE
dc.date.available2012-12-17T08:35:20Zde_DE
dc.date.issued2012-12-
dc.identifier.other732372224de_DE
dc.identifier.urihttp://tubdok.tub.tuhh.de/handle/11420/1084-
dc.description.abstractWe generalize an augmented rounding error result that was proven for the symmetric Lanczos process in [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2347--2359], to the two-sided (usually unsymmetric) Lanczos process for tridiagonalizing a square matrix. We extend the analysis to more general perturbations than rounding errors in order to provide tools for the analysis of inexact and related methods. The aim is to develop a deeper understanding of the behavior of all these methods. Our results take the same form as those for the symmetric Lanczos process, except for the bounds on the backward perturbation terms (the generalizations of backward rounding errors for the augmented system). In general we cannot derive tight a priori bounds for these terms as was done for the symmetric process, but a posteriori bounds are feasible, while bounds related to certain properties of matrices would be theoretically desirable.en
dc.language.isoende_DE
dc.relation.ispartofseriesPreprints des Institutes für Mathematik;Bericht 169-
dc.rightsinfo:eu-repo/semantics/openAccess-
dc.rights.urihttp://doku.b.tu-harburg.de/doku/lic_mit_pod.phpde
dc.subjectLanczos-Prozessde_DE
dc.subjectendliche Genauigkeitde_DE
dc.subjectPerturbationsanalyse, Nicht-Hermitische Matrixde_DE
dc.subjectVerlust der Biorthogonalitätde_DE
dc.subjectLanczos processde_DE
dc.subjectfinite precisionde_DE
dc.subjectperturbation analysis, non-Hermitian matrixde_DE
dc.subjectLoss of bi-orthogonalityde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleAn augmented analysis of the perturbed two-sided Lanczos tridiagonalization processde_DE
dc.typePreprintde_DE
dc.identifier.urnurn:nbn:de:gbv:830-tubdok-11795de_DE
dc.identifier.doi10.15480/882.1082-
dc.type.dinipreprint-
dc.subject.gndLanczos-Verfahrende
dc.subject.gndKrylov-Verfahrende
dc.subject.gndSchwach besetzte Matrixde
dc.subject.ddccode510-
dc.subject.msc65F15:Eigenvalues, eigenvectorsen
dc.subject.msccode65F15-
dcterms.DCMITypeText-
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tuhh.gvk.ppn732372224de_DE
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tuhh.pod.urlhttp://www.epubli.de/oai/tu-hamburg/1179?idp=urn:nbn:de:gbv:830-tubdok-11795de_DE
tuhh.pod.allowedtruede_DE
dc.identifier.hdl11420/1084-
tuhh.abstract.englishWe generalize an augmented rounding error result that was proven for the symmetric Lanczos process in [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2347--2359], to the two-sided (usually unsymmetric) Lanczos process for tridiagonalizing a square matrix. We extend the analysis to more general perturbations than rounding errors in order to provide tools for the analysis of inexact and related methods. The aim is to develop a deeper understanding of the behavior of all these methods. Our results take the same form as those for the symmetric Lanczos process, except for the bounds on the backward perturbation terms (the generalizations of backward rounding errors for the augmented system). In general we cannot derive tight a priori bounds for these terms as was done for the symmetric process, but a posteriori bounds are feasible, while bounds related to certain properties of matrices would be theoretically desirable.de_DE
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.1082-
tuhh.type.opusPreprint (Vorabdruck)-
tuhh.institute.germanMathematik E-10de
tuhh.institute.englishMathematics E-10en
tuhh.institute.id47de_DE
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tuhh.series.namePreprints des Institutes für Mathematik-
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tuhh.relation.ispartofseriesPreprints des Institutes für Mathematikde_DE
tuhh.relation.ispartofseriesnumber169de_DE
item.grantfulltextopen-
item.languageiso639-1en-
item.creatorOrcidPaige, Christopher C.-
item.creatorOrcidPanayotov, Ivo-
item.creatorOrcidZemke, Jens-Peter M.-
item.cerifentitytypePublications-
item.openairetypePreprint-
item.creatorGNDPaige, Christopher C.-
item.creatorGNDPanayotov, Ivo-
item.creatorGNDZemke, Jens-Peter M.-
item.seriesrefPreprints des Institutes für Mathematik;169-
item.mappedtypePreprint-
item.tuhhseriesidPreprints des Institutes für Mathematik-
item.openairecristypehttp://purl.org/coar/resource_type/c_816b-
item.fulltextWith Fulltext-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0002-5748-8727-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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