Publication:
A simplified approach to Fiedler-like pencils via block minimal bases pencils

dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Matemática Aplicada a Control, Sistemas y Señaleses
dc.contributor.authorBueno Cachadiña, María Isabel
dc.contributor.authorMartínez Dopico, Froilán César
dc.contributor.authorPerez, J.
dc.contributor.authorSaavedra, R.
dc.contributor.authorZykoski, B.
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-04-06T07:33:34Z
dc.date.available2021-04-06T07:33:34Z
dc.date.issued2018-06-15
dc.description.abstractThe standard way of solving the polynomial eigenvalue problem associated with a matrix polynomial is to embed the matrix coefficients of the polynomial into a matrix pencil, transforming the problem into an equivalent generalized eigenvalue problem. Such pencils are known as linearizations. Many of the families of linearizations for matrix polynomials available in the literature are extensions of the so-called family of Fiedler pencils. These families are known as generalized Fiedler pencils, Fiedler pencils with repetition, and generalized Fiedler pencils with repetition or Fiedler like pencils for simplicity. The goal of this work is to unify the Fiedler-like pencils approach with the more recent one based on strong block minimal bases pencils introduced in F.M. Dopico et al. (2017). To this end, we introduce a family of pencils that we have named extended block Kronecker pencils, whose members are, under some generic nonsingularity conditions, strong block minimal bases pencils, and show that, with the exception of the non-proper generalized Fiedler pencils, all Fiedler-like pencils belong to this family modulo permutations. As a consequence of this result, we obtain a much simpler theory for Fiedler-like pencils than the one available so far. Moreover, we expect this simplification to allow for further developments in the theory of Fiedler-like pencils such as global or local backward error analyses and eigenvalue conditioning analyses of polynomial eigenvalue problems solved via Fiedler-like linearizations.en
dc.format.extent60
dc.identifier.bibliographicCitationBueno, M. I., Dopico, F. M., Pérez, J., Saavedra, R. & Zykoski, B. (2018). A simplified approach to Fiedler-like pencils via block minimal bases pencils. Linear Algebra and Its Applications, 547, pp. 45–104.en
dc.identifier.doihttps://doi.org/10.1016/j.laa.2018.01.033
dc.identifier.issn0024-3795
dc.identifier.publicationfirstpage45
dc.identifier.publicationlastpage104
dc.identifier.publicationtitleLinear Algebra and Its Applicationsen
dc.identifier.publicationvolume547
dc.identifier.urihttps://hdl.handle.net/10016/32265
dc.identifier.uxxiAR/0000021444
dc.language.isoengen
dc.publisherElsevieren
dc.relation.projectIDGobierno de España. MTM2015-65798-Pes
dc.relation.projectIDGobierno de España. MTM2015-68805-REDTes
dc.rights© 2018 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.otherFiedler pencilsen
dc.subject.otherGeneralized Fiedler pencilsen
dc.subject.otherFiedler pencils with repetitionen
dc.subject.otherGeneralized Fiedler pencils with repetitionen
dc.subject.otherMatrix polynomialsen
dc.subject.otherStrong linearizationsen
dc.subject.otherBlock minimal bases pencilsen
dc.subject.otherBlock Kronecker pencilsen
dc.subject.otherExtended block Kronecker pencilsen
dc.subject.otherMinimal basisen
dc.subject.otherDual minimal basesen
dc.titleA simplified approach to Fiedler-like pencils via block minimal bases pencilsen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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