Publicação
A Monte Carlo method for computing the action of a matrix exponential on a vector
| Resumo: | A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a given continuous-time Markov chain. The vector solution is computed probabilistically by averaging over a suitable multiplicative functional. This representation extends the existing linear algebra Monte Carlo-based methods, and was used in practice to develop an efficient algorithm capable of computing both, a single entry or the full vector solution. Finally, several relevant benchmarks were executed to assess the performance of the algorithm. A comparison with the results obtained with a Krylov-based method shows the remarkable performance of the algorithm for solving large-scale problems. |
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| Autores principais: | Acebron, J. A. |
| Assunto: | Monte Carlo methods Communicability Matrix functions Network analysis |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | ISCTE |
| Idioma: | inglês |
| Origem: | Repositório ISCTE |
| Resumo: | A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a given continuous-time Markov chain. The vector solution is computed probabilistically by averaging over a suitable multiplicative functional. This representation extends the existing linear algebra Monte Carlo-based methods, and was used in practice to develop an efficient algorithm capable of computing both, a single entry or the full vector solution. Finally, several relevant benchmarks were executed to assess the performance of the algorithm. A comparison with the results obtained with a Krylov-based method shows the remarkable performance of the algorithm for solving large-scale problems. |
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