Artigo em revista científica Q1
A Monte Carlo method for computing the action of a matrix exponential on a vector
Juan Torres (Acebron, J. A.);
Título Revista
Applied Mathematics and Computation
Ano (publicação definitiva)
2019
Língua
Inglês
País
Países Baixos (Holanda)
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Abstract/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.
Agradecimentos/Acknowledgements
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Palavras-chave
Monte Carlo methods,Communicability,Matrix functions,Network analysis
  • Matemáticas - Ciências Naturais
Registos de financiamentos
Referência de financiamento Entidade Financiadora
UID/CEC/50021/2019 Fundação para a Ciência e a Tecnologia