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dc.contributor.authorAcebrón de Torres, Juan A.
dc.contributor.authorHerrero Zaragoza, José Ramón
dc.contributor.authorMonteiro, José
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Arquitectura de Computadors
dc.identifier.citationAcebrón, J.; Herrero, J.; Monteiro, J. A highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel Monte Carlo method. "Computers & mathematics with applications", 1 Gener 2020, vol. 79, núm. 12, p. 3495-3515.
dc.description.abstractA novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths which evolve through the indices of the matrix according to a suitable probability law. The computational complexity is proved in this paper to be significantly better than the classical Monte Carlo method, which allows the computation of much more accurate solutions. Furthermore, the positive features of the algorithm in terms of parallelism were exploited in practice to develop a highly scalable implementation capable of solving some test problems very efficiently using high performance supercomputers equipped with a large number of cores. For the specific case of shared memory architectures the performance of the algorithm was compared with the results obtained using an available Krylov-based algorithm, outperforming the latter in all benchmarks analyzed so far.
dc.description.sponsorshipThe work has been performed under the Project HPC-EUROPA3 (INFRAIA-2016-1-730897), with the support of the EC Research Innovation Action under the H2020 Programme; in particular, the authors gratefully acknowledge the support of the Computer Architecture Department at Universitat Politècnica de Catalunya (UPC), Spain and the computer resources and technical support provided by Barcelona Supercomputing Center (BSC), Spain. We acknowledge PRACE, Belgium for awarding us access to Marconi at CINECA, through grant 2010PA4246. This work was also supported by Fundação para a Ciência e a Tecnologia, Portugal under Grant No. UIDB/50021/2020, by the Spanish Ministry of Science and Technology through TIN2015-65316-P project and by the Generalitat de Catalunya, Spain (contract 2017-SGR-1414).
dc.format.extent21 p.
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International
dc.rights©2020 Elsevier
dc.subjectÀrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat
dc.subject.lcshMonte Carlo method
dc.subject.lcshParallel algorithms
dc.subject.otherExponential integrators
dc.subject.otherMatrix functions
dc.subject.otherNetwork analysis
dc.subject.otherHigh performance computing
dc.titleA highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel Monte Carlo method
dc.subject.lemacMontecarlo, Mètode de
dc.subject.lemacAlgorismes paral·lels
dc.contributor.groupUniversitat Politècnica de Catalunya. CAP - Grup de Computació d'Altes Prestacions
dc.description.peerreviewedPeer Reviewed
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/AGAUR/2017 SGR 1414
local.citation.authorAcebrón, J.; Herrero, J.; Monteiro, J.
local.citation.publicationNameComputers & mathematics with applications

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