A Monte Carlo method for computing the action of a matrix exponential on a vector
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.
Cite
@article{arxiv.1904.12759,
title = {A Monte Carlo method for computing the action of a matrix exponential on a vector},
author = {Juan A. Acebron},
journal= {arXiv preprint arXiv:1904.12759},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1904.12754