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Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation

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Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation

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dc.contributor.author Bader, Philipp es_ES
dc.contributor.author Blanes Zamora, Sergio es_ES
dc.contributor.author Casas, Fernando es_ES
dc.date.accessioned 2020-04-06T08:56:40Z
dc.date.available 2020-04-06T08:56:40Z
dc.date.issued 2019-12 es_ES
dc.identifier.uri http://hdl.handle.net/10251/140219
dc.description.abstract [EN] A new way to compute the Taylor polynomial of a matrix exponential is presented which reduces the number of matrix multiplications in comparison with the de-facto standard Paterson-Stockmeyer method for polynomial evaluation. Combined with the scaling and squaring procedure, this reduction is sufficient to make the Taylor method superior in performance to Pade approximants over a range of values of the matrix norms. An efficient adjustment to make the method robust against overscaling is also introduced. Numerical experiments show the superior performance of our method to have a similar accuracy in comparison with state-of-the-art implementations, and thus, it is especially recommended to be used in conjunction with Lie-group and exponential integrators where preservation of geometric properties is at issue. es_ES
dc.description.sponsorship This work was funded by Ministerio de Economia, Industria y Competitividad (Spain) through project MTM2016-77660-P (AEI/FEDER, UE). P.B. was additionally supported by a contract within the Program Juan de la Cierva Formacion (Spain). es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Mathematics es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Exponential of a matrix es_ES
dc.subject Scaling and squaring es_ES
dc.subject Matrix polynomials es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/math7121174 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2016-77660-P/ES/NUEVOS RETOS EN INTEGRACION NUMERICA: FUNDAMENTOS ALGEBRAICOS, METODOS DE ESCISION, METODOS DE MONTECARLO Y OTRAS APLICACIONES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Bader, P.; Blanes Zamora, S.; Casas, F. (2019). Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation. Mathematics. 7(12):1-19. https://doi.org/10.3390/math7121174 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/math7121174 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 19 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 7 es_ES
dc.description.issue 12 es_ES
dc.identifier.eissn 2227-7390 es_ES
dc.relation.pasarela S\402247 es_ES
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
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