Please use this identifier to cite or link to this item:
http://hdl.handle.net/10071/19104
Author(s): | Acebron, J. A. |
Date: | 2019 |
Title: | A Monte Carlo method for computing the action of a matrix exponential on a vector |
Volume: | 362 |
Pages: | 1 - 13 |
ISSN: | 0096-3003 |
DOI (Digital Object Identifier): | 10.1016/j.amc.2019.06.059 |
Keywords: | Monte Carlo methods Communicability Matrix functions Network analysis |
Abstract: | 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. |
Peerreviewed: | yes |
Access type: | Open Access |
Appears in Collections: | CTI-RI - Artigos em revistas científicas internacionais com arbitragem científica |
Files in This Item:
File | Description | Size | Format | |
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exp_MC_resub.pdf | Pós-print | 311,75 kB | Adobe PDF | View/Open |
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