Strong Linearizations of Rational Matrices

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Show simple item record Amparan, A. Martínez Dopico, Froilán César Marcaida, Silvia Zaballa, I. 2021-03-22T12:07:27Z 2021-03-22T12:07:27Z 2018-11-20
dc.identifier.bibliographicCitation Amparan, A., Dopico, F. M., Marcaida, S. & Zaballa, I. (2018). Strong Linearizations of Rational Matrices. SIAM Journal on Matrix Analysis and Applications, 39(4), pp. 1670–1700.
dc.identifier.issn 0895-4798
dc.description.abstract This paper defines for the first time strong linearizations of arbitrary rational matrices, studies in depth properties and characterizations of such linear matrix pencils, and develops infinitely many examples of strong linearizations that can be explicitly and easily constructed from a minimal state-space realization of the strictly proper part of the considered rational matrix and the coefficients of the polynomial part. As a consequence, the results in this paper establish a rigorous foundation for the numerical computation of the complete structure of zeros and poles, both finite and at infinity, of any rational matrix by applying any well-known backward stable algorithm for generalized eigenvalue problems to any of the strong linearizations constructed in this work.
dc.format.extent 31
dc.language.iso eng
dc.publisher Society for Industrial and Applied Mathematics (SIAM)
dc.rights © 2018, Society for Industrial and Applied Mathematics
dc.subject.other Linearization
dc.subject.other Minimal polynomial system matrix
dc.subject.other Nonlinear eigenvalue problem
dc.subject.other Rational matrix
dc.subject.other Strong block minimal bases linearization
dc.subject.other Strong linearization
dc.title Strong Linearizations of Rational Matrices
dc.type article
dc.subject.eciencia Matemáticas
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012-32542
dc.relation.projectID Gobierno de España. MTM2013-40960-P
dc.relation.projectID Gobierno de España. MTM2015-65798-P
dc.relation.projectID Gobierno de España. MTM2017-83624-P
dc.relation.projectID Gobierno de España. MTM2015-68805-REDT
dc.relation.projectID Gobierno de España. MTM2017-90682-REDT
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 1670
dc.identifier.publicationissue 4
dc.identifier.publicationlastpage 1700
dc.identifier.publicationtitle SIAM Journal on Matrix Analysis and Applications
dc.identifier.publicationvolume 39
dc.identifier.uxxi AR/0000022351
dc.contributor.funder Ministerio de Economía, Industria y Competitividad (España)
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