Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis

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Show simple item record Martínez Dopico, Froilán César Marcaida, Silvia Quintana Ponce, Maria Del Carmen 2021-04-06T10:45:41Z 2019-06-01
dc.identifier.bibliographicCitation Dopico, F. M., Marcaida, S. & Quintana, M. C. (2019). Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis. Linear Algebra and Its Applications, 570, pp. 1–45.
dc.identifier.issn 0024-3795
dc.description.abstract We construct a new family of strong linearizations of rational matrices considering the polynomial part of them expressed in a basis that satisfies a three term recurrence relation. For this purpose, we combine the theory developed by Amparan et al. (2018), and the new linearizations of polynomial matrices introduced by Fa(sic)bender and Saltenberger (2017). In addition, we present a detailed study of how to recover eigenvectors of a rational matrix from those of its linearizations in this family. We complete the paper by discussing how to extend the results when the polynomial part is expressed in other bases, and by presenting strong linearizations that preserve the structure of symmetric or Hermitian rational matrices. A conclusion of this work is that the combination of the results in this paper with those in Amparan et al. (2018), allows us to use essentially all the strong linearizations of polynomial matrices developed in the last fifteen years to construct strong linearizations of any rational matrix by expressing such a matrix in terms of its polynomial and strictly proper parts.
dc.format.extent 45
dc.language.iso eng
dc.publisher Elsevier
dc.rights © 2019 Elsevier Inc.
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.subject.other Rational matrix
dc.subject.other Rational eigenvalue problem
dc.subject.other Strong block minimal bases pencil
dc.subject.other Strong linearization
dc.subject.other Recovery of eigenvectors
dc.subject.other Symmetric strong linearization
dc.subject.other Hermitian strong linearization
dc.subject.other Vector-spaces
dc.subject.other Krylov methods
dc.subject.other Minimal bases
dc.title Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights embargoedAccess
dc.relation.projectID Gobierno de España. MTM2015-65798-P
dc.relation.projectID Gobierno de España. BES-2016-076744
dc.relation.projectID Gobierno de España. MTM2017-90682-REDT
dc.relation.projectID Gobierno de España. MTM2017-83624-P
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1
dc.identifier.publicationlastpage 45
dc.identifier.publicationtitle Linear Algebra and Its Applications
dc.identifier.publicationvolume 570
dc.identifier.uxxi AR/0000023493
carlosiii.embargo.liftdate 2021-06-01
carlosiii.embargo.terms 2021-06-01
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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