On the singular two-parameter eigenvalue problem II

Košir, Tomaž (author), Plestenjak, Bor (author)

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.

• Language: English
• Keywords: singular two-parameter eigenvalue problem, Kronecker canonical form, minimal reducing subspace, stratification
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2022
• Number of pages: Str. 433-451
• Numbering: Vol. 649
• PID: 20.500.12556/RUL-139719
• UDC: 512.643:519.6
• ISSN on article: 0024-3795
• DOI: 10.1016/j.laa.2022.05.013
• COBISS.SI-ID: 111311363
• Publication date in RUL: 06.09.2022

Record is a part of a journal

• Title: Linear algebra and its applications
• Shortened title: Linear algebra appl.
• Publisher: North Holland
• ISSN: 0024-3795
• COBISS.SI-ID: 1119247

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

• Language: Slovenian
• Keywords: singularni dvoparametrični problem lastnih vrednosti, Kroneckerjeva kanonična oblika, minimalni reducirajoči podprostor, stratifikacija

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: N1-0154
• Name: Verjetnostne metode za skupne in singularne probleme lastnih vrednosti