Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.1800
DC FieldValueLanguage
dc.contributor.authorBetcke, Marta-
dc.contributor.authorVoß, Heinrich-
dc.date.accessioned2018-10-29T12:42:43Z-
dc.date.available2018-10-29T12:42:43Z-
dc.date.issued2016-05-14-
dc.identifier.citationNumerische Mathematik 2 (135): 397-430 (2017)de_DE
dc.identifier.issn0945-3245de_DE
dc.identifier.urihttp://tubdok.tub.tuhh.de/handle/11420/1803-
dc.description.abstractIn this work we present a new restart technique for iterative projection methods for nonlinear eigenvalue problems admitting minmax characterization of their eigenvalues. Our technique makes use of the minmax induced local enumeration of the eigenvalues in the inner iteration. In contrast to global numbering which requires including all the previously computed eigenvectors in the search subspace, the proposed local numbering only requires a presence of one eigenvector in the search subspace. This effectively eliminates the search subspace growth and therewith the super-linear increase of the computational costs if a large number of eigenvalues or eigenvalues in the interior of the spectrum are to be computed. The new restart technique is integrated into nonlinear iterative projection methods like the Nonlinear Arnoldi and Jacobi-Davidson methods. The efficiency of our new restart framework is demonstrated on a range of nonlinear eigenvalue problems: quadratic, rational and exponential including an industrial real-life conservative gyroscopic eigenvalue problem modeling free vibrations of a rolling tire. We also present an extension of the method to problems without minmax property but with eigenvalues which have a dominant either real or imaginary part and test it on two quadratic eigenvalue problems.en
dc.language.isoende_DE
dc.publisherSpringerde_DE
dc.relation.ispartofNumerische Mathematikde_DE
dc.rightsCC BY 4.0de_DE
dc.rightsinfo:eu-repo/semantics/openAccess-
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectIterative projection methodde_DE
dc.subjectJacobi-Davidson methodde_DE
dc.subjectminmax characterizationde_DE
dc.subjectnonlinear Arnoldi methodde_DE
dc.subjectnonlinear eigenvalue problemde_DE
dc.subjectrestartde_DE
dc.subjectpurge and lockde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleRestarting iterative projection methods for Hermitian nonlinear eigenvalue problems with minmax propertyde_DE
dc.typeArticlede_DE
dc.identifier.urnurn:nbn:de:gbv:830-88223408-
dc.identifier.doi10.15480/882.1800-
dc.type.diniarticle-
dc.subject.ddccode510-
dcterms.DCMITypeText-
tuhh.identifier.urnurn:nbn:de:gbv:830-88223408de_DE
tuhh.oai.showtrue-
dc.identifier.hdl11420/1803-
tuhh.abstract.englishIn this work we present a new restart technique for iterative projection methods for nonlinear eigenvalue problems admitting minmax characterization of their eigenvalues. Our technique makes use of the minmax induced local enumeration of the eigenvalues in the inner iteration. In contrast to global numbering which requires including all the previously computed eigenvectors in the search subspace, the proposed local numbering only requires a presence of one eigenvector in the search subspace. This effectively eliminates the search subspace growth and therewith the super-linear increase of the computational costs if a large number of eigenvalues or eigenvalues in the interior of the spectrum are to be computed. The new restart technique is integrated into nonlinear iterative projection methods like the Nonlinear Arnoldi and Jacobi-Davidson methods. The efficiency of our new restart framework is demonstrated on a range of nonlinear eigenvalue problems: quadratic, rational and exponential including an industrial real-life conservative gyroscopic eigenvalue problem modeling free vibrations of a rolling tire. We also present an extension of the method to problems without minmax property but with eigenvalues which have a dominant either real or imaginary part and test it on two quadratic eigenvalue problems.de_DE
tuhh.publisher.doi10.1007/s00211-016-0804-3-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.identifier.doi10.15480/882.1800-
tuhh.type.opus(wissenschaftlicher) Artikel-
tuhh.institute.germanMathematik E-10de
tuhh.institute.englishMathematik E-10de_DE
tuhh.gvk.hasppnfalse-
tuhh.hasurnfalse-
openaire.rightsinfo:eu-repo/semantics/openAccessde_DE
dc.type.driverarticle-
dc.rights.ccversion4.0de_DE
dc.type.casraiJournal Article-
tuhh.container.issue2de_DE
tuhh.container.volume135de_DE
tuhh.container.startpage397de_DE
tuhh.container.endpage430de_DE
dc.rights.nationallicensefalsede_DE
dc.identifier.scopus2-s2.0-84968561527-
local.funding.infoEPSRC Postdoctoral Fellowship (Grant Number EP/H02865X/1)de_DE
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.grantfulltextopen-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.creatorOrcidBetcke, Marta-
item.creatorOrcidVoß, Heinrich-
item.languageiso639-1en-
item.creatorGNDBetcke, Marta-
item.creatorGNDVoß, Heinrich-
item.fulltextWith Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.mappedtypeArticle-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0003-3818-2121-
crisitem.author.orcid0000-0003-2394-375X-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik (E)-
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