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Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation
dc.contributor.author | Bader, Philipp | |
dc.contributor.author | Blanes, Sergio | |
dc.contributor.author | Casas, Fernando | |
dc.date.accessioned | 2020-03-24T11:38:43Z | |
dc.date.available | 2020-03-24T11:38:43Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | BADER, Philipp; BLANES, Sergio; CASAS, Fernando. Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation. Mathematics, 2019, vol. 7, no 12, p. 1174. | ca_CA |
dc.identifier.issn | 2227-7390 | |
dc.identifier.uri | http://hdl.handle.net/10234/187081 | |
dc.description.abstract | 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 Padé 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. | ca_CA |
dc.format.extent | 19 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | MDPI | ca_CA |
dc.relation.isPartOf | Mathematics 2019, 7, 1174. | ca_CA |
dc.rights | © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). | ca_CA |
dc.rights | Atribución 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-sa/4.0/ | * |
dc.subject | exponential of a matrix | ca_CA |
dc.subject | scaling and squaring | ca_CA |
dc.subject | matrix polynomials | ca_CA |
dc.title | Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | http://dx.doi.org/10.3390/math7121174 | |
dc.relation.projectID | MTM2016-77660-P (AEI/FEDER, UE) | ca_CA |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.relation.publisherVersion | https://www.mdpi.com/2227-7390/7/12/1174 | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
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