Academic Journal
On the singular two-parameter eigenvalue problem II
| Τίτλος: | On the singular two-parameter eigenvalue problem II |
|---|---|
| Συγγραφείς: | Košir, Tomaž, Plestenjak, Bor |
| Πηγή: | Linear algebra and its applications, vol. 649, pp. 433-451, 2022. ; ISSN: 0024-3795 |
| Στοιχεία εκδότη: | Elsevier |
| Έτος έκδοσης: | 2022 |
| Συλλογή: | University of Ljubljana: Repository (RUJ) / Repozitorij Univerze v Ljubljani |
| Θεματικοί όροι: | singular two-parameter eigenvalue problem, Kronecker canonical form, minimal reducing subspace, stratification, singularni dvoparametrični problem lastnih vrednosti, Kroneckerjeva kanonična oblika, minimalni reducirajoči podprostor, stratifikacija, info:eu-repo/classification/udc/512.643:519.6 |
| Περιγραφή: | In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems, which is a key relation for many theoretical results and numerical methods for nonsingular multiparameter eigenvalue problems. In 2009, Muhič and Plestenjak extended the above relation to a class of singular two-parameter eigenvalue problems with coprime characteristic polynomials and such that all finite eigenvalues are algebraically simple. They introduced a way to solve a singular two-parameter eigenvalue problem by computing the common regular eigenvalues of the associated system of two singular generalized eigenvalue problems. Using new tools, in particular the stratification theory, we extend this connection to singular two-parameter eigenvalue problems with possibly multiple eigenvalues and such that characteristic polynomials can have a nontrivial common factor. |
| Τύπος εγγράφου: | article in journal/newspaper |
| Περιγραφή αρχείου: | application/pdf; text/url |
| Γλώσσα: | English |
| Relation: | info:eu-repo/grantAgreement/ARRS//N1-0154; https://plus.cobiss.net/cobiss/si/sl/bib/111311363 |
| Διαθεσιμότητα: | https://repozitorij.uni-lj.si/IzpisGradiva.php?id=139719 https://repozitorij.uni-lj.si/Dokument.php?id=160325&dn= https://repozitorij.uni-lj.si/Dokument.php?id=160324&dn= https://plus.cobiss.net/cobiss/si/sl/bib/111311363 https://hdl.handle.net/20.500.12556/RUL-139719 |
| Rights: | http://creativecommons.org/licenses/by-nc-nd/4.0/ ; info:eu-repo/semantics/openAccess |
| Αριθμός Καταχώρησης: | edsbas.AB0BDEC0 |
| Βάση Δεδομένων: | BASE |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://repozitorij.uni-lj.si/IzpisGradiva.php?id=139719# Name: EDS - BASE (ns324271) Category: fullText Text: View record from BASE |
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| Items | – Name: Title Label: Title Group: Ti Data: On the singular two-parameter eigenvalue problem II – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Košir%2C+Tomaž%22">Košir, Tomaž</searchLink><br /><searchLink fieldCode="AR" term="%22Plestenjak%2C+Bor%22">Plestenjak, Bor</searchLink> – Name: TitleSource Label: Source Group: Src Data: Linear algebra and its applications, vol. 649, pp. 433-451, 2022. ; ISSN: 0024-3795 – Name: Publisher Label: Publisher Information Group: PubInfo Data: Elsevier – Name: DatePubCY Label: Publication Year Group: Date Data: 2022 – Name: Subset Label: Collection Group: HoldingsInfo Data: University of Ljubljana: Repository (RUJ) / Repozitorij Univerze v Ljubljani – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22singular+two-parameter+eigenvalue+problem%22">singular two-parameter eigenvalue problem</searchLink><br /><searchLink fieldCode="DE" term="%22Kronecker+canonical+form%22">Kronecker canonical form</searchLink><br /><searchLink fieldCode="DE" term="%22minimal+reducing+subspace%22">minimal reducing subspace</searchLink><br /><searchLink fieldCode="DE" term="%22stratification%22">stratification</searchLink><br /><searchLink fieldCode="DE" term="%22singularni+dvoparametrični+problem+lastnih+vrednosti%22">singularni dvoparametrični problem lastnih vrednosti</searchLink><br /><searchLink fieldCode="DE" term="%22Kroneckerjeva+kanonična+oblika%22">Kroneckerjeva kanonična oblika</searchLink><br /><searchLink fieldCode="DE" term="%22minimalni+reducirajoči+podprostor%22">minimalni reducirajoči podprostor</searchLink><br /><searchLink fieldCode="DE" term="%22stratifikacija%22">stratifikacija</searchLink><br /><searchLink fieldCode="DE" term="%22info%3Aeu-repo%2Fclassification%2Fudc%2F512%2E643%3A519%2E6%22">info:eu-repo/classification/udc/512.643:519.6</searchLink> – Name: Abstract Label: Description Group: Ab Data: In the 1960s, Atkinson introduced an abstract algebraic setting for multiparameter eigenvalue problems. He showed that a nonsingular multiparameter eigenvalue problem is equivalent to the associated system of generalized eigenvalue problems, which is a key relation for many theoretical results and numerical methods for nonsingular multiparameter eigenvalue problems. In 2009, Muhič and Plestenjak extended the above relation to a class of singular two-parameter eigenvalue problems with coprime characteristic polynomials and such that all finite eigenvalues are algebraically simple. They introduced a way to solve a singular two-parameter eigenvalue problem by computing the common regular eigenvalues of the associated system of two singular generalized eigenvalue problems. Using new tools, in particular the stratification theory, we extend this connection to singular two-parameter eigenvalue problems with possibly multiple eigenvalues and such that characteristic polynomials can have a nontrivial common factor. – Name: TypeDocument Label: Document Type Group: TypDoc Data: article in journal/newspaper – Name: Format Label: File Description Group: SrcInfo Data: application/pdf; text/url – Name: Language Label: Language Group: Lang Data: English – Name: NoteTitleSource Label: Relation Group: SrcInfo Data: info:eu-repo/grantAgreement/ARRS//N1-0154; https://plus.cobiss.net/cobiss/si/sl/bib/111311363 – Name: URL Label: Availability Group: URL Data: https://repozitorij.uni-lj.si/IzpisGradiva.php?id=139719<br />https://repozitorij.uni-lj.si/Dokument.php?id=160325&dn=<br />https://repozitorij.uni-lj.si/Dokument.php?id=160324&dn=<br />https://plus.cobiss.net/cobiss/si/sl/bib/111311363<br />https://hdl.handle.net/20.500.12556/RUL-139719 – Name: Copyright Label: Rights Group: Cpyrght Data: http://creativecommons.org/licenses/by-nc-nd/4.0/ ; info:eu-repo/semantics/openAccess – Name: AN Label: Accession Number Group: ID Data: edsbas.AB0BDEC0 |
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| RecordInfo | BibRecord: BibEntity: Languages: – Text: English Subjects: – SubjectFull: singular two-parameter eigenvalue problem Type: general – SubjectFull: Kronecker canonical form Type: general – SubjectFull: minimal reducing subspace Type: general – SubjectFull: stratification Type: general – SubjectFull: singularni dvoparametrični problem lastnih vrednosti Type: general – SubjectFull: Kroneckerjeva kanonična oblika Type: general – SubjectFull: minimalni reducirajoči podprostor Type: general – SubjectFull: stratifikacija Type: general – SubjectFull: info:eu-repo/classification/udc/512.643:519.6 Type: general Titles: – TitleFull: On the singular two-parameter eigenvalue problem II Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Košir, Tomaž – PersonEntity: Name: NameFull: Plestenjak, Bor IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2022 Identifiers: – Type: issn-locals Value: edsbas – Type: issn-locals Value: edsbas.oa Titles: – TitleFull: Linear algebra and its applications, vol. 649, pp. 433-451, 2022. ; ISSN: 0024-3795 Type: main |
| ResultId | 1 |