A comparison of eigenvalue condition numbers for matrix polynomials

Anguas Márquez, Luis Miguel; Bueno Cachadiña, María Isabel; Martínez Dopico, Froilán César

Publication:
A comparison of eigenvalue condition numbers for matrix polynomials

dc.affiliation.dpto	UC3M. Departamento de Matemáticas	es
dc.affiliation.grupoinv	UC3M. Grupo de Investigación: Matemática Aplicada a Control, Sistemas y Señales	es
dc.contributor.author	Anguas Márquez, Luis Miguel
dc.contributor.author	Bueno Cachadiña, María Isabel
dc.contributor.author	Martínez Dopico, Froilán César
dc.contributor.funder	Ministerio de Economía y Competitividad (España)	es
dc.date.accessioned	2021-04-06T09:38:46Z
dc.date.available	2021-04-06T09:38:46Z
dc.date.issued	2019-03-01
dc.description.abstract	In this paper, we consider the different condition numbers for simple eigenvalues of matrix polynomials used in the literature and we compare them. One of these condition numbers is a generalization of the Wilkinson condition number for the standard eigenvalue problem. This number has the disadvantage of only being defined for finite eigenvalues. In order to give a unified approach to all the eigenvalues of a matrix polynomial, both finite and infinite, two (homogeneous) condition numbers have been defined in the literature. In their definition, very different approaches are used. One of the main goals of this note is to show that, when the matrix polynomial has a moderate degree, both homogeneous condition numbers are essentially the same and one of them provides a geometric interpretation of the other. We also show how the homogeneous condition numbers compare with the "Wilkinson-like" eigenvalue condition number and how they extend this condition number to zero and infinite eigenvalues. .	en
dc.format.extent	31
dc.identifier.bibliographicCitation	Anguas, L. M., Bueno, M. I. & Dopico, F. M. (2019). A comparison of eigenvalue condition numbers for matrix polynomials. Linear Algebra and Its Applications, 564, pp. 170–200.	en
dc.identifier.doi	https://doi.org/10.1016/j.laa.2018.11.031
dc.identifier.issn	0024-3795
dc.identifier.publicationfirstpage	170
dc.identifier.publicationlastpage	200
dc.identifier.publicationtitle	Linear Algebra and Its Applications	en
dc.identifier.publicationvolume	564
dc.identifier.uri	https://hdl.handle.net/10016/32269
dc.identifier.uxxi	AR/0000023050
dc.language.iso	eng	en
dc.publisher	Elsevier	en
dc.relation.projectID	Gobierno de España. MTM2015-65798-P	es
dc.relation.projectID	Gobierno de España. MTM2017-90682-REDT	es
dc.relation.projectID	Gobierno de España. BES-2013-065688	es
dc.rights	© 2018 Elsevier Inc.	en
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España	*
dc.rights.accessRights	open access	en
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/	*
dc.subject.eciencia	Matemáticas	es
dc.subject.other	Eigenvalue condition number	en
dc.subject.other	Matrix polynomial	en
dc.subject.other	Chordal distance	en
dc.subject.other	Eigenvalue	en
dc.title	A comparison of eigenvalue condition numbers for matrix polynomials	en
dc.type	research article	*
dc.type.hasVersion	AM	*
dspace.entity.type	Publication