DC Field | Value | Language |
---|---|---|
dc.contributor.author | Meerbergen, Karl | - |
dc.contributor.author | Schröder, Christian | - |
dc.contributor.author | Voß, Heinrich | - |
dc.date.accessioned | 2020-06-12T10:57:02Z | - |
dc.date.available | 2020-06-12T10:57:02Z | - |
dc.date.issued | 2012-07-09 | - |
dc.identifier.citation | Numerical Linear Algebra with Applications 5 (20): 852-868 (2013-10-01) | de_DE |
dc.identifier.issn | 1099-1506 | de_DE |
dc.identifier.uri | http://hdl.handle.net/11420/6302 | - |
dc.description.abstract | The 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.iso | en | de_DE |
dc.publisher | Wiley | de_DE |
dc.relation.ispartof | Numerical linear algebra with applications | de_DE |
dc.subject | Critical delay | de_DE |
dc.subject | Delay-differential equation | de_DE |
dc.subject | Jacobi-Davidson | de_DE |
dc.subject | Nonlinear eigenvalue problem | de_DE |
dc.subject | Two-parameter eigenvalue problem | de_DE |
dc.subject.ddc | 510: Mathematik | de_DE |
dc.title | A Jacobi-Davidson method for two-real-parameter nonlinear eigenvalue problems arising from delay-differential equations | de_DE |
dc.type | Article | de_DE |
dc.type.dini | article | - |
dcterms.DCMIType | Text | - |
tuhh.abstract.english | The 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.doi | 10.1002/nla.1848 | - |
tuhh.publication.institute | Mathematik E-10 | de_DE |
tuhh.type.opus | (wissenschaftlicher) Artikel | - |
dc.type.driver | article | - |
dc.type.casrai | Journal Article | - |
tuhh.container.issue | 5 | de_DE |
tuhh.container.volume | 20 | de_DE |
tuhh.container.startpage | 852 | de_DE |
tuhh.container.endpage | 868 | de_DE |
dc.relation.project | Interuniversity Attraction Poles Program | de_DE |
dc.identifier.scopus | 2-s2.0-84883811079 | - |
local.status.inpress | false | de_DE |
local.funding.info | Belgian State Science Policy Office | de_DE |
local.funding.info | Research Council K.U. Leuven | de_DE |
local.funding.info | MATHEON, the DFG research Center in Berlin | de_DE |
datacite.resourceType | Journal Article | - |
datacite.resourceTypeGeneral | Text | - |
item.languageiso639-1 | en | - |
item.grantfulltext | none | - |
item.creatorOrcid | Meerbergen, Karl | - |
item.creatorOrcid | Schröder, Christian | - |
item.creatorOrcid | Voß, Heinrich | - |
item.mappedtype | Article | - |
item.creatorGND | Meerbergen, Karl | - |
item.creatorGND | Schröder, Christian | - |
item.creatorGND | Voß, Heinrich | - |
item.fulltext | No Fulltext | - |
item.openairetype | Article | - |
item.openairecristype | http://purl.org/coar/resource_type/c_6501 | - |
item.cerifentitytype | Publications | - |
crisitem.author.dept | Mathematik E-10 | - |
crisitem.author.orcid | 0000-0003-2394-375X | - |
crisitem.author.parentorg | Studiendekanat Elektrotechnik, Informatik und Mathematik | - |
Appears in Collections: | Publications without fulltext |
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