Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.100
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dc.contributor.authorZemke, Jens-Peter M.-
dc.date.accessioned2006-02-01T11:37:22Zde_DE
dc.date.available2006-02-01T11:37:22Zde_DE
dc.date.issued2005-07-
dc.identifier.urihttp://tubdok.tub.tuhh.de/handle/11420/102-
dc.description.abstractWe introduce the framework of abstract perturbed Krylov methods''. This is a new and unifying point of view on Krylov subspace methods based solely on the matrix equation $AQ_k+F_k=Q_{k+1}underline{C}_k=Q_kC_k+q_{k+1}c_{k+1,k}e_k^T$ and the assumption that the matrix $C_k$ is unreduced Hessenberg. We give polynomial expressions relating the Ritz vectors, (Q)OR iterates and (Q)MR iterates to the starting vector $q_1$ and the perturbation terms ${f_l}_{l=1}^k$. The properties of these polynomials and similarities between them are analyzed in some detail. The results suggest the interpretation of abstract perturbed Krylov methods as additive overlay of several abstract exact Krylov methods.en
dc.language.isoende_DE
dc.relation.ispartofseriesPreprints des Institutes für Mathematik:Bericht 89-
dc.rightsinfo:eu-repo/semantics/openAccess-
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectAbstract perturbed Krylov methodde_DE
dc.subjectinexact Krylov methodde_DE
dc.subjectfinite precisionde_DE
dc.subjectHessenberg matrixde_DE
dc.subjectbasis polynomialde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleAbstract perturbed Krylov methodsde_DE
dc.typePreprintde_DE
dc.date.updated2006-02-01T11:37:32Zde_DE
dc.identifier.urnurn:nbn:de:gbv:830-opus-1587de_DE
dc.identifier.doi10.15480/882.100-
dc.type.dinipreprint-
dc.subject.gndKrylov-Verfahrende
dc.subject.ddccode510-
dc.subject.msc65F20:Overdetermined systems, pseudoinversesen
dc.subject.msc65F15:Eigenvalues, eigenvectorsen
dc.subject.msc15A15:Determinants, permanents, other special matrix functionsen
dc.subject.msc65F10:Iterative methods for linear systemsen
dc.subject.msc15A24:Matrix equations and identitiesen
dc.subject.msc65Y20:Complexity and performance of numerical algorithmsen
dc.subject.msccode65F15-
dc.subject.msccode15A24-
dc.subject.msccode65F10-
dc.subject.msccode15A15-
dc.subject.msccode65F20-
dc.subject.msccode65Y20-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-opus-1587de_DE
tuhh.publikation.typreportde_DE
tuhh.opus.id158de_DE
tuhh.oai.showtruede_DE
dc.identifier.hdl11420/102-
tuhh.abstract.englishWe introduce the framework of abstract perturbed Krylov methods''. This is a new and unifying point of view on Krylov subspace methods based solely on the matrix equation $AQ_k+F_k=Q_{k+1}underline{C}_k=Q_kC_k+q_{k+1}c_{k+1,k}e_k^T$ and the assumption that the matrix $C_k$ is unreduced Hessenberg. We give polynomial expressions relating the Ritz vectors, (Q)OR iterates and (Q)MR iterates to the starting vector $q_1$ and the perturbation terms ${f_l}_{l=1}^k$. The properties of these polynomials and similarities between them are analyzed in some detail. The results suggest the interpretation of abstract perturbed Krylov methods as additive overlay of several abstract exact Krylov methods.de_DE
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.100-
tuhh.type.opusPreprint (Vorabdruck)-
tuhh.institute.germanMathematik E-10de
tuhh.institute.englishMathematics E-10en
tuhh.institute.id47de_DE
tuhh.type.id20de_DE
tuhh.gvk.hasppnfalse-
tuhh.series.id20-
tuhh.series.namePreprints des Institutes für Mathematik-
dc.type.driverpreprint-
dc.identifier.oclc930767805-
dc.type.casraiOther-
tuhh.relation.ispartofseriesPreprints des Institutes für Mathematikde_DE
tuhh.relation.ispartofseriesnumber89de_DE
datacite.resourceTypeOther-
datacite.resourceTypeGeneralText-
item.grantfulltextopen-
item.openairecristypehttp://purl.org/coar/resource_type/c_816b-
item.creatorGNDZemke, Jens-Peter M.-
item.openairetypePreprint-
item.tuhhseriesidPreprints des Institutes für Mathematik-
item.fulltextWith Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidZemke, Jens-Peter M.-
item.languageiso639-1en-
item.seriesrefPreprints des Institutes für Mathematik;89-
item.mappedtypePreprint-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0002-5748-8727-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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