A highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel Monte Carlo method
View/Open
Acebron+et+al.pdf (364,8Kb) (Restricted access)
Request copy
Què és aquest botó?
Aquest botó permet demanar una còpia d'un document restringit a l'autor. Es mostra quan:
- Disposem del correu electrònic de l'autor
- El document té una mida inferior a 20 Mb
- Es tracta d'un document d'accés restringit per decisió de l'autor o d'un document d'accés restringit per política de l'editorial
Cita com:
hdl:2117/187864
Document typeArticle
Defense date2020-01-01
Rights accessRestricted access - publisher's policy
(embargoed until 2022-03-05)
Abstract
A 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.
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.
ISSN0898-1221
Publisher versionhttps://www.sciencedirect.com/science/article/pii/S0898122120300808
Other identifiershttps://arxiv.org/abs/1904.12754
Files | Description | Size | Format | View |
---|---|---|---|---|
Acebron+et+al.pdf![]() | 364,8Kb | Restricted access |
Except where otherwise noted, content on this work
is licensed under a Creative Commons license
:
Attribution-NonCommercial-NoDerivs 4.0 Generic