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New bounds for roots of polynomials based on Fiedler companion matrices

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Interdisciplinar de Sistemas Complejos (GISC)es
dc.contributor.authorTerán Vergara, Fernando de
dc.contributor.authorMartínez Dopico, Froilán César
dc.contributor.authorPérez Álvaro, Javier
dc.date.accessioned2015-12-09T11:17:47Z
dc.date.available2016-06-16T22:00:08Z
dc.date.issued2014-06-15
dc.description.abstractSeveral matrix norms of the classical Frobenius companion matrices of a monic polynomial p(z) have been used in the literature to obtain simple lower and upper bounds on the absolute values of the roots lambda of p(z). Recently, M. Fiedler (2003) [9] has introduced a new family of companion matrices of p(z) that has received considerable attention and it is natural to investigate if matrix norms of Fiedler companion matrices may be used to obtain new and sharper lower and upper bounds on vertical bar lambda vertical bar. The development of such bounds requires first to know simple expressions for some relevant matrix norms of Fiedler matrices and we obtain them in the case of the 1- and infinity-matrix norms. With these expressions at hand, we will show that norms of Fiedler matrices produce many new bounds, but that none of them improves significatively the classical bounds obtained from the Frobenius companion matrices. However, we will prove that if the norms of the inverses of Fiedler matrices are used, then another family of new bounds on vertical bar lambda vertical bar is obtained and some of the bounds in this family improve significatively the bounds coming from the Frobenius companion matrices for certain polynomials.es
dc.description.sponsorshipThis work has been supported by the Ministerio de Economía y Competitividad of Spain through grant MTM2012-32542.es
dc.format.extent22es
dc.format.mimetypeapplication/pdf
dc.identifier.bibliographicCitationLinear Algebra and its Applications, 451 (2014) 15 June, pp. 197-230es
dc.identifier.doi10.1016/j.laa.2014.03.013
dc.identifier.issn0024-3795
dc.identifier.publicationfirstpage197es
dc.identifier.publicationissue15 Junees
dc.identifier.publicationlastpage230es
dc.identifier.publicationtitleLinear algebra and its applicationses
dc.identifier.publicationvolume451es
dc.identifier.urihttps://hdl.handle.net/10016/22078
dc.identifier.uxxiAR/0000015197
dc.publisherElsevieres
dc.relation.projectIDGobierno de España. MTM-2012-32542es
dc.relation.publisherversionhttp://dx.doi.org/10.1016/j.laa.2014.03.013es
dc.rights© 2014 Elsevieres
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accesses
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherBoundses
dc.subject.otherEigenvalueses
dc.subject.otherFiedler companion matriceses
dc.subject.otherMatrix normses
dc.subject.otherRoots of polynomialses
dc.titleNew bounds for roots of polynomials based on Fiedler companion matriceses
dc.typeresearch article*
dspace.entity.typePublication
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