Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.175
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dc.contributor.authorVoß, Heinrich-
dc.date.accessioned2006-03-02T11:56:58Zde_DE
dc.date.available2006-03-02T11:56:58Zde_DE
dc.date.issued1998-11-
dc.identifier.urihttp://tubdok.tub.tuhh.de/handle/11420/177-
dc.description.abstractIn a recent paper Melman [12] derived upper bounds for the smallest eigenvalue of a real symmetric Toeplitz matrix in terms of the smallest roots of rational and polynomial approximations of the secular equation $f(lambda)=0$, the best of which being constructed by the $(1,2)$-Pad{accent19 e} approximation of $f$. In this paper we prove that this bound is the smallest eigenvalue of the projection of the given eigenvalue problem onto a Krylov space of $T_n^{-1}$ of dimension 3. This interpretation of the bound suggests enhanced bounds of increasing accuracy. They can be substantially improved further by exploiting symmetry properties of the principal eigenvector of $T_n$.en
dc.language.isoende_DE
dc.rightsinfo:eu-repo/semantics/openAccess-
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectToeplitz matrixde_DE
dc.subjecteigenvalue problemde_DE
dc.subjectsymmetryde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleBounds for the minimum eigenvalue of a symmetric Toeplitz matrixde_DE
dc.typeWorking Paperde_DE
dc.date.updated2006-03-02T11:56:58Zde_DE
dc.identifier.urnurn:nbn:de:gbv:830-opus-2395de_DE
dc.identifier.doi10.15480/882.175-
dc.type.diniworkingPaper-
dc.subject.gndToeplitz-Matrixde
dc.subject.gndEigenwertproblemde
dc.subject.ddccode510-
dc.subject.msc65F15:Eigenvalues, eigenvectorsen
dc.subject.msccode65F15-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-opus-2395de_DE
tuhh.publikation.typworkingPaperde_DE
tuhh.opus.id239de_DE
tuhh.oai.showtruede_DE
dc.identifier.hdl11420/177-
tuhh.abstract.englishIn a recent paper Melman [12] derived upper bounds for the smallest eigenvalue of a real symmetric Toeplitz matrix in terms of the smallest roots of rational and polynomial approximations of the secular equation $f(lambda)=0$, the best of which being constructed by the $(1,2)$-Pad{accent19 e} approximation of $f$. In this paper we prove that this bound is the smallest eigenvalue of the projection of the given eigenvalue problem onto a Krylov space of $T_n^{-1}$ of dimension 3. This interpretation of the bound suggests enhanced bounds of increasing accuracy. They can be substantially improved further by exploiting symmetry properties of the principal eigenvector of $T_n$.de_DE
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.175-
tuhh.type.opusResearchPaper-
tuhh.institute.germanMathematik E-10de
tuhh.institute.englishMathematics E-10en
tuhh.institute.id47de_DE
tuhh.type.id17de_DE
tuhh.gvk.hasppnfalse-
dc.type.driverworkingPaper-
dc.identifier.oclc930768112-
dc.type.casraiWorking Paper-
tuhh.relation.ispartofseriesPreprints des Institutes für Mathematikde_DE
tuhh.relation.ispartofseriesnumber20de_DE
datacite.resourceTypeWorking Paper-
datacite.resourceTypeGeneralText-
item.grantfulltextopen-
item.openairecristypehttp://purl.org/coar/resource_type/c_8042-
item.creatorGNDVoß, Heinrich-
item.openairetypeWorking Paper-
item.tuhhseriesidPreprints des Institutes für Mathematik-
item.fulltextWith Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidVoß, Heinrich-
item.languageiso639-1en-
item.seriesrefPreprints des Institutes für Mathematik;20-
item.mappedtypeWorking Paper-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0003-2394-375X-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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