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A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error

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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.authorBueno Cachadiña, María Isabel
dc.contributor.authorMartínez Dopico, Froilán César
dc.contributor.authorFurtado, S.
dc.contributor.authorMedina, L.
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2021-03-18T10:46:44Z
dc.date.available2021-03-18T10:46:44Z
dc.date.issued2018-09
dc.description.abstractThe standard way of solving numerically a polynomial eigenvalue problem (PEP) is to use a linearization and solve the corresponding generalized eigenvalue problem (GEP). In addition, if the PEP possesses one of the structures arising very often in applications, then the use of a linearization that preserves such structure combined with a structured algorithm for the GEP presents considerable numerical advantages. Block-symmetric linearizations have proven to be very useful for constructing structured linearizations of structured matrix polynomials. In this scenario, we analyze the eigenvalue condition numbers and backward errors of approximated eigenpairs of a block symmetric linearization that was introduced by Fiedler (Linear Algebra Appl 372:325-331, 2003) for scalar polynomials and generalized to matrix polynomials by Antoniou and Vologiannidis (Electron J Linear Algebra 11:78-87, 2004). This analysis reveals that such linearization has much better numerical properties than any other block-symmetric linearization analyzed so far in the literature, including those in the well known vector space of block-symmetric linearizations. The main drawback of the analyzed linearization is that it can be constructed only for matrix polynomials of odd degree, but we believe that it will be possible to extend its use to even degree polynomials via some strategies in the near future.en
dc.format.extent43
dc.identifier.bibliographicCitationBueno, M. I., Dopico, F. M., Furtado, S., Medina, L. (2018). A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error. Calcolo, 55(3).en
dc.identifier.doihttps://doi.org/10.1007/s10092-018-0273-4
dc.identifier.issn0008-0624
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue3
dc.identifier.publicationlastpage43
dc.identifier.publicationtitleCalcolo
dc.identifier.publicationvolume55
dc.identifier.urihttps://hdl.handle.net/10016/32176
dc.identifier.uxxiAR/0000021689
dc.language.isoeng
dc.publisherSpringer Natureen
dc.relation.projectIDGobierno de España. MTM2015-65798-Pes
dc.rights© 2018, Istituto di Informatica e Telematica del Consiglio Nazionale delle Ricercheen
dc.rights.accessRightsopen access
dc.subject.ecienciaMatemáticases
dc.subject.otherBackward error of an approximate eigenpairen
dc.subject.otherBlock-symmetric linearizationen
dc.subject.otherConditioning of an eigenvalueen
dc.subject.otherEigenvalueen
dc.subject.otherEigenvectoren
dc.subject.otherLinearizationen
dc.subject.otherMatrix polynomialen
dc.subject.otherStrong linearizationen
dc.titleA block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward erroren
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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