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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.contributor.author | Seydaoglu, Muaz![]() |
es_ES |
dc.date.accessioned | 2023-03-27T18:01:38Z | |
dc.date.available | 2023-03-27T18:01:38Z | |
dc.date.issued | 2022-04 | es_ES |
dc.identifier.issn | 0378-4754 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/192628 | |
dc.description.abstract | [EN] We present a practical algorithm to approximate the exponential of skew-Hermitian matrices up to round-off error based on an efficient computation of Chebyshev polynomials of matrices and the corresponding error analysis. It is based on Chebyshev polynomials of degrees 2, 4, 8, 12 and 18 which are computed with only 1, 2, 3, 4 and 5 matrix-matrix products, respectively. For problems of the form exp(-i A), with A a real and symmetric matrix, an improved version is presented that computes the sine and cosine of A with a reduced computational cost. The theoretical analysis, supported by numerical experiments, indicates that the new methods are more efficient than schemes based on rational Pade approximants and Taylor polynomials for all tolerances and time interval lengths. The new procedure is particularly recommended to be used in conjunction with exponential integrators for the numerical time integration of the Schrodinger equation. | es_ES |
dc.description.sponsorship | SB and FC have been supported by Ministerio de Ciencia e Innovacion (Spain) through project PID2019-104927GB-C21 (AEI/FEDER, UE). The work of MS has been funded by the Scientific and Technological Research Council of Turkey (TUBITAK) with Grant Number 1059B191802292. SB and FC would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme "Geometry, compatibility and structure preservation in computational differential equations", when work on this paper was undertaken. This work was been additionally supported by EPSRC, United Kingdom Grant Number EP/R014604/1. The authors wish to thank the referee for his/her detailed list of comments and suggestions which were most helpful to improve the presentation of the paper. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Elsevier | es_ES |
dc.relation.ispartof | Mathematics and Computers in Simulation | es_ES |
dc.rights | Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) | es_ES |
dc.subject | Matrix exponential | es_ES |
dc.subject | Matrix sine | es_ES |
dc.subject | Matrix cosine | es_ES |
dc.subject | Matrix polynomials | es_ES |
dc.subject | Schrodinger equation | es_ES |
dc.subject.classification | MATEMATICA APLICADA | es_ES |
dc.title | An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrodinger equation | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.1016/j.matcom.2021.12.002 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104927GB-C21/ES/METODOS DE INTEGRACION GEOMETRICA PARA PROBLEMAS CUANTICOS, MECANICA CELESTE Y SIMULACIONES MONTECARLO I/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/EPSRC//EP%2FR014604%2F1/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/TUBITAK//1059B191802292/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/MICINN//PID2019-104927GB-C21//METODOS DE INTEGRACION GEOMETRICA PARA PROBLEMAS CUANTICOS, MECANICA CELESTE Y SIMULACIONES MONTECARLO I/ | es_ES |
dc.rights.accessRights | Abierto | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería del Diseño - Escola Tècnica Superior d'Enginyeria del Disseny | es_ES |
dc.description.bibliographicCitation | Bader, P.; Blanes Zamora, S.; Casas, F.; Seydaoglu, M. (2022). An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrodinger equation. Mathematics and Computers in Simulation. 194:383-400. https://doi.org/10.1016/j.matcom.2021.12.002 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.1016/j.matcom.2021.12.002 | es_ES |
dc.description.upvformatpinicio | 383 | es_ES |
dc.description.upvformatpfin | 400 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 194 | es_ES |
dc.relation.pasarela | S\485814 | es_ES |
dc.contributor.funder | European Regional Development Fund | es_ES |
dc.contributor.funder | Ministerio de Ciencia e Innovación | es_ES |
dc.contributor.funder | Scientific and Technological Research Council of Turkey | es_ES |
dc.contributor.funder | Engineering and Physical Sciences Research Council, Reino Unido | es_ES |