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

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Matemática Aplicada a Control, Sistemas y Señaleses
dc.contributor.authorMartínez Dopico, Froilán César
dc.contributor.authorMarcaida, Silvia
dc.contributor.authorQuintana Ponce, María del Carmen
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-04-06T10:45:41Z
dc.date.available2021-06-01T23:00:04Z
dc.date.issued2019-06-01
dc.description.abstractWe 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.en
dc.format.extent45
dc.identifier.bibliographicCitationDopico, 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.en
dc.identifier.doihttps://doi.org/10.1016/j.laa.2019.02.003
dc.identifier.issn0024-3795
dc.identifier.publicationfirstpage1
dc.identifier.publicationlastpage45
dc.identifier.publicationtitleLinear Algebra and Its Applicationsen
dc.identifier.publicationvolume570
dc.identifier.urihttps://hdl.handle.net/10016/32272
dc.identifier.uxxiAR/0000023493
dc.language.isoengen
dc.publisherElsevieren
dc.relation.projectIDGobierno de España. MTM2015-65798-Pes
dc.relation.projectIDGobierno de España. BES-2016-076744es
dc.relation.projectIDGobierno de España. MTM2017-90682-REDTes
dc.relation.projectIDGobierno de España. MTM2017-83624-Pes
dc.rights© 2019 Elsevier Inc.en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherRational matrixen
dc.subject.otherRational eigenvalue problemen
dc.subject.otherStrong block minimal bases pencilen
dc.subject.otherStrong linearizationen
dc.subject.otherRecovery of eigenvectorsen
dc.subject.otherSymmetric strong linearizationen
dc.subject.otherHermitian strong linearizationen
dc.subject.otherVector-spacesen
dc.subject.otherKrylov methodsen
dc.subject.otherMinimal basesen
dc.titleStrong linearizations of rational matrices with polynomial part expressed in an orthogonal basisen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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