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Efficient evaluation of matrix polynomials

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Efficient evaluation of matrix polynomials

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dc.contributor.author Sastre, Jorge es_ES
dc.date.accessioned 2019-09-05T20:03:55Z
dc.date.available 2019-09-05T20:03:55Z
dc.date.issued 2018 es_ES
dc.identifier.issn 0024-3795 es_ES
dc.identifier.uri http://hdl.handle.net/10251/125088
dc.description.abstract [EN] This paper presents a new family of methods for evaluating matrix polynomials more efficiently than the state-of-the-art Paterson-Stockmeyer method. Examples of the application of the methods to the Taylor polynomial approximation of matrix functions like the matrix exponential and matrix cosine are given. Their efficiency is compared with that of the best existing evaluation schemes for general polynomial and rational approximations, and also with a recent method based on mixed rational and polynomial approximants. For many years, the Paterson-Stockmeyer method has been considered the most efficient general method for the evaluation of matrix polynomials. In this paper we show that this statement is no longer true. Moreover, for many years rational approximations have been considered more efficient than polynomial approximations, although recently it has been shown that often this is not the case in the computation of the matrix exponential and matrix cosine. In this paper we show that in fact polynomial approximations provide a higher order of approximation than the state-of-the-art computational methods for rational approximations for the same cost in terms of matrix products. (C) 2017 Elsevier Inc. All rights reserved. es_ES
dc.description.sponsorship This work has been supported by Spanish Ministerio de Economia y Competitividad and European Regional Development Fund (ERDF) grant TIN2014-59294-P. We thank the anonymous referee who revised this paper so thoroughly and carefully. es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation MINECO/TIN2014-59294-P es_ES
dc.relation.ispartof Linear Algebra and its Applications es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Matrix es_ES
dc.subject Polynomial es_ES
dc.subject Rational es_ES
dc.subject Mixed rational and polynomial es_ES
dc.subject Approximation es_ES
dc.subject Computation es_ES
dc.subject Matrix function es_ES
dc.subject.classification TEORIA DE LA SEÑAL Y COMUNICACIONES es_ES
dc.title Efficient evaluation of matrix polynomials es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.laa.2017.11.010 es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Comunicaciones - Departament de Comunicacions es_ES
dc.description.bibliographicCitation Sastre, J. (2018). Efficient evaluation of matrix polynomials. Linear Algebra and its Applications. 539:229-250. https://doi.org/10.1016/j.laa.2017.11.010 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1016/j.laa.2017.11.010 es_ES
dc.description.upvformatpinicio 229 es_ES
dc.description.upvformatpfin 250 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 539 es_ES
dc.relation.pasarela S\387731 es_ES
dc.contributor.funder Ministerio de Economía y Empresa es_ES


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