Academic Journal
On the singular two-parameter eigenvalue problem II
| Title: | On the singular two-parameter eigenvalue problem II |
|---|---|
| Authors: | Košir, Tomaž, Plestenjak, Bor |
| Source: | Linear algebra and its applications, vol. 649, pp. 433-451, 2022. ; ISSN: 0024-3795 |
| Publisher Information: | Elsevier |
| Publication Year: | 2022 |
| Collection: | University of Ljubljana: Repository (RUJ) / Repozitorij Univerze v Ljubljani |
| Subject Terms: | 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 |
| Description: | 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. |
| Document Type: | article in journal/newspaper |
| File Description: | application/pdf; text/url |
| Language: | English |
| Relation: | info:eu-repo/grantAgreement/ARRS//N1-0154; https://plus.cobiss.net/cobiss/si/sl/bib/111311363 |
| Availability: | 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 |
| Accession Number: | edsbas.AB0BDEC0 |
| Database: | BASE |
| Description not available. |