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## A highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel Monte Carlo method

Author
Acebrón, J.; Herrero, J.; Monteiro, J.
Type of activity
Journal article
Journal
Computers & mathematics with applications
Date of publication
2020-01-01
Volume
79
Number
12
First page
3495
Last page
3515
DOI
10.1016/j.camwa.2020.02.013
Project funding
High performance computing VII
Models de programació i entorns d'execució paral·lels
Repository
http://hdl.handle.net/2117/187864
https://arxiv.org/abs/1904.12754
URL
https://www.sciencedirect.com/science/article/pii/S0898122120300808
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 so...
Citation
Acebrón, 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.
Keywords
Exponential integrators, High performance computing, Matrix functions, Multilevel Monte Carlo method, Network analysis, Parallel algorithms
Group of research
CAP - High Performace Computing Group
inLab FIB