Algebraic linearizations of matrix polynomials

Authors
Chan, Eunice Y.S.; Corless, Robert M.; González Vega, Laureano; Sendra Pons, Juan RafaelUniversity of Alcalá Author; Sendra Pons, JuanaUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49681
DOI: 10.1016/j.laa.2018.10.028
ISSN: 0024-3795
Publisher
Elsevier
Date
2019-02-15
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Economía y Competitividad
Bibliographic citation
Chan, E.Y.S., Corless, R.M., González Vega, L., Sendra, J.R. & Sendra, J. 2019, “Algebraic linearizations of matrix polynomials”, Linear Algebra and its Applications, vol. 563, pp. 373-399.
Keywords
Companion matrices
Linearization
Matrix polynomials
Block upper Hessenberg
Description / Notes
Part of this work was developed while R.M.Corless was visiting the University of Alcalá, in the frame of the project Giner de los Rios. We acknowledge the support of the Ontario Graduate Institution, the National Science & Engineering Research Council of Canada, the University of Alcalá, the Rotman Institute of Philosophy, the Ontario Research Centre of Computer Algebra, and Western Univ.
Project
info:eu-repo/grantAgreement/MINECO//MTM2014-54141-P/ES/CONSTRUCCIONES ALGEBRO-GEOMETRICAS: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
https://doi.org/10.1016/j.laa.2018.10.028
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2018 Elsevier
Access rights
info:eu-repo/semantics/openAccess
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Abstract
We show how to construct linearizations of matrix polynomials za(z)d0+c0, a(z)b(z), a(z) +b(z)(when deg (b(z))<deg (a(z))), and za(z)d0b(z) +c0from linearizations of the component parts, a(z)and b(z). This allows the extension to matrix polynomials of a new companion matrix construction.
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