Linearizations of matrix polynomials viewed as Rosenbrock's system matrices

Autor:	Froilán M. Dopico, Silvia Marcaida, María C. Quintana, Paul Van Dooren
Rok vydání:	2023
Předmět:	Numerical Analysis Algebra and Number Theory FOS: Mathematics Discrete Mathematics and Combinatorics 15A22 15A54 93B18 93C05 Mathematics - Numerical Analysis Numerical Analysis (math.NA) Geometry and Topology
Zdroj:	Linear Algebra and its Applications.
ISSN:	0024-3795
DOI:	10.1016/j.laa.2023.05.010
Popis:	A well known method to solve the Polynomial Eigenvalue Problem (PEP) is via linearization. That is, transforming the PEP into a generalized linear eigenvalue problem with the same spectral information and solving such linear problem with some of the eigenvalue algorithms available in the literature. Linearizations of matrix polynomials are usually defined using unimodular transformations. In this paper we establish a connection between the standard definition of linearization for matrix polynomials introduced by Gohberg, Lancaster and Rodman and the notion of polynomial system matrix introduced by Rosenbrock. This connection gives new techniques to show that a matrix pencil is a linearization of the corresponding matrix polynomial arising in a PEP.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::324581ff82ea2506791cb2010dfa5547 https://doi.org/10.1016/j.laa.2023.05.010 Zobrazit plný text záznamu Full Text from ScienceDirect