Linearizations of Hermitian Matrix Polynomials Preserving the Sign Characteristic

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dc.contributor.author Bueno, Maria I.
dc.contributor.author Martínez Dopico, Froilán César
dc.contributor.author Furtado, Susanna
dc.date.accessioned 2021-03-18T10:01:53Z
dc.date.available 2021-03-18T10:01:53Z
dc.date.issued 2017
dc.identifier.bibliographicCitation Bueno, M. I., Dopico, F. M., Furtado, S. (2017). Linearizations of Hermitian Matrix Polynomials Preserving the Sign Characteristic. SIAM Journal on Matrix Analysis and Applications, 38(1), pp. 249–272.
dc.identifier.issn 0895-4798
dc.identifier.uri http://hdl.handle.net/10016/32172
dc.description.abstract The development of strong linearizations preserving whatever structure a matrix polynomial might possess has been a very active area of research in the last years, since such linearizations are the starting point of numerical algorithms for computing eigenvalues of structured matrix polynomials with the properties imposed by the considered structure. In this context, Hermitian matrix polynomials are one of the most important classes of matrix polynomials arising in applications and their real eigenvalues are of great interest. The sign characteristic is a set of signs attached to these real eigenvalues which is crucial for determining the behavior of systems described by Hermitian matrix polynomials and, therefore, it is desirable to develop linearizations that preserve the sign characteristic of these polynomials, but, at present, only one such linearization is known. In this paper, we present a complete characterization of all the Hermitian strong linearizations that preserve the sign characteristic of a given Hermitian matrix polynomial and identify several families of such linearizations that can be constructed very easily from the coefficients of the polynomial.
dc.format.extent 24
dc.language.iso eng
dc.publisher Society for Industrial and Applied Mathematics (SIAM)
dc.rights © 2017, Society for Industrial and Applied Mathematics
dc.subject.other Congruence
dc.subject.other Generalized fiedler pencil
dc.subject.other Hermitian matrix polynomial
dc.subject.other Sign characteristic
dc.subject.other Linearization
dc.subject.other Strong linearization
dc.subject.other Structured strong linearizations
dc.subject.other Eigenvalue problems
dc.subject.other Fiedler pencils
dc.subject.other Vector-spaces
dc.subject.other Minimal bases
dc.subject.other Smith forms
dc.subject.other Eigenvectors
dc.subject.other Equivalence
dc.subject.other Pairs
dc.title Linearizations of Hermitian Matrix Polynomials Preserving the Sign Characteristic
dc.type article
dc.subject.eciencia Matemáticas
dc.identifier.doi https://doi.org/10.1137/151004847
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012-32542
dc.relation.projectID Gobierno de España. MTM2015-65798-P
dc.relation.projectID Gobierno de España. MTM2015-68805-REDT
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 249
dc.identifier.publicationissue 1
dc.identifier.publicationlastpage 272
dc.identifier.publicationtitle SIAM Journal on Matrix Analysis and Applications
dc.identifier.publicationvolume 38
dc.identifier.uxxi AR/0000019876
dc.contributor.funder Ministerio de Economía y Competitividad (España)
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