DC FieldValueLanguage
dc.contributor.authorMeerbergen, Karl-
dc.contributor.authorSchröder, Christian-
dc.contributor.authorVoß, Heinrich-
dc.date.accessioned2020-06-12T10:57:02Z-
dc.date.available2020-06-12T10:57:02Z-
dc.date.issued2012-07-09-
dc.identifier.citationNumerical Linear Algebra with Applications 5 (20): 852-868 (2013-10-01)de_DE
dc.identifier.issn1099-1506de_DE
dc.identifier.urihttp://hdl.handle.net/11420/6302-
dc.description.abstractThe critical delays of a delay-differential equation can be computed by solving a nonlinear two-parameter eigenvalue problem. The solution of this two-parameter problem can be translated to solving a quadratic eigenvalue problem of squared dimension. We present a structure preserving QR-type method for solving such quadratic eigenvalue problem that only computes real-valued critical delays; that is, complex critical delays, which have no physical meaning, are discarded. For large-scale problems, we propose new correction equations for a Newton-type or Jacobi-Davidson style method, which also forces real-valued critical delays. We present three different equations: one real-valued equation using a direct linear system solver, one complex valued equation using a direct linear system solver, and one Jacobi-Davidson style correction equation that is suitable for an iterative linear system solver. We show numerical examples for large-scale problems arising from PDEs. © 2012 John Wiley & Sons, Ltd.en
dc.language.isoende_DE
dc.publisherWileyde_DE
dc.relation.ispartofNumerical linear algebra with applicationsde_DE
dc.subjectCritical delayde_DE
dc.subjectDelay-differential equationde_DE
dc.subjectJacobi-Davidsonde_DE
dc.subjectNonlinear eigenvalue problemde_DE
dc.subjectTwo-parameter eigenvalue problemde_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleA Jacobi-Davidson method for two-real-parameter nonlinear eigenvalue problems arising from delay-differential equationsde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishThe critical delays of a delay-differential equation can be computed by solving a nonlinear two-parameter eigenvalue problem. The solution of this two-parameter problem can be translated to solving a quadratic eigenvalue problem of squared dimension. We present a structure preserving QR-type method for solving such quadratic eigenvalue problem that only computes real-valued critical delays; that is, complex critical delays, which have no physical meaning, are discarded. For large-scale problems, we propose new correction equations for a Newton-type or Jacobi-Davidson style method, which also forces real-valued critical delays. We present three different equations: one real-valued equation using a direct linear system solver, one complex valued equation using a direct linear system solver, and one Jacobi-Davidson style correction equation that is suitable for an iterative linear system solver. We show numerical examples for large-scale problems arising from PDEs. © 2012 John Wiley & Sons, Ltd.de_DE
tuhh.publisher.doi10.1002/nla.1848-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issue5de_DE
tuhh.container.volume20de_DE
tuhh.container.startpage852de_DE
tuhh.container.endpage868de_DE
dc.relation.projectInteruniversity Attraction Poles Programde_DE
dc.identifier.scopus2-s2.0-84883811079-
local.status.inpressfalsede_DE
local.funding.infoBelgian State Science Policy Officede_DE
local.funding.infoResearch Council K.U. Leuvende_DE
local.funding.infoMATHEON, the DFG research Center in Berlinde_DE
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.languageiso639-1en-
item.grantfulltextnone-
item.creatorOrcidMeerbergen, Karl-
item.creatorOrcidSchröder, Christian-
item.creatorOrcidVoß, Heinrich-
item.mappedtypeArticle-
item.creatorGNDMeerbergen, Karl-
item.creatorGNDSchröder, Christian-
item.creatorGNDVoß, Heinrich-
item.fulltextNo Fulltext-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.cerifentitytypePublications-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0003-2394-375X-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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