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Title: A probabilistic linear solver based on a multilevel Monte Carlo Method
Authors: Acebron, J. A.
Keywords: Multilevel
Monte Carlo method
Network analysis
Parallel algorithms
High performance computing
Issue Date: 2020
Publisher: Springer/Plenum Publishers
Abstract: We describe a new Monte Carlo method based on a multilevel method for computing the action of the resolvent matrix over a vector. The method is based on the numerical evaluation of the Laplace transform of the matrix exponential, which is computed efficiently using a multilevel Monte Carlo method. Essentially, it requires generating suitable random paths which evolve through the indices of the matrix according to the probability law of a continuous-time Markov chain governed by the associated Laplacian matrix. The convergence of the proposed multilevel method has been discussed, and several numerical examples were run to test the performance of the algorithm. These examples concern the computation of some metrics of interest in the analysis of complex networks, and the numerical solution of a boundary-value problem for an elliptic partial differential equation. In addition, the algorithm was conveniently parallelized, and the scalability analyzed and compared with the results of other existing Monte Carlo method for solving linear algebra systems.
Peer reviewed: yes
DOI: 10.1007/s10915-020-01168-2
ISSN: 0885-7474
Accession number: WOS:000517999900002
Appears in Collections:CTI-RI - Artigos em revistas científicas internacionais com arbitragem científica

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