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Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems

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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.authorVan Dooren, Paul
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-04-07T09:38:33Z
dc.date.available2022-11-01T00:00:06Z
dc.date.issued2020-11-01
dc.description.abstractThis paper presents a definition for local linearizations of rational matrices and studies their properties. This definition allows to introduce matrix pencils associated to a rational matrix that preserve its structure of zeros and poles in subsets of any algebraically closed field and also at infinity. This new theory of local linearizations captures and explains rigorously the properties of all the different pencils that have been used from the 1970's until 2020 for computing zeros, poles and eigenvalues of rational matrices. Particular attention is paid to those pencils that have appeared recently in the numerical solution of nonlinear eigenvalue problems through rational approximation.en
dc.format.extent35
dc.identifier.bibliographicCitationDopico, F. M., Marcaida, S., Quintana, M. C. & Van Dooren, P. (2020). Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems. Linear Algebra and Its Applications, 604, pp. 441–475.en
dc.identifier.doihttps://doi.org/10.1016/j.laa.2020.07.004
dc.identifier.issn0024-3795
dc.identifier.publicationfirstpage441
dc.identifier.publicationlastpage475
dc.identifier.publicationtitleLinear Algebra and Its Applicationsen
dc.identifier.publicationvolume604
dc.identifier.urihttps://hdl.handle.net/10016/32289
dc.identifier.uxxiAR/0000027194
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. PID2019-106362GB-I00es
dc.relation.projectIDGobierno de España. MTM2017-90682-REDTes
dc.relation.projectIDGobierno de España. MTM2017-83624-Pes
dc.rights© 2020 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.otherNonlinear eigenvalue problemen
dc.subject.otherLinearizationen
dc.subject.otherPolynomial system matrixen
dc.subject.otherRational approximationen
dc.subject.otherBlock full rank pencilsen
dc.titleLocal linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problemsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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