RT Journal Article
T1 An Efficient Algorithm for Accelerating Monte Carlo Approximations of the Solution to Boundary Value Problems
A1 Mancini, Sara
A1 Bernal Martínez, Francisco Manuel
A1 Acebrón, Juan Antonio
AB The numerical approximation of boundary value problems by means of a probabilistic representations often has the drawback that the Monte Carlo estimate of the solution is substantially biased due to the presence of the domain boundary. We introduce a scheme, which we have called the leading-term Monte Carlo regression, which seeks to remove that bias by replacing a ’cloud’ of Monte Carlo estimates—carried out at different discretization levels—for the usual single Monte Carlo estimate. The practical result of our scheme is an acceleration of the Monte Carlo method. Theoretical analysis of the proposed scheme, confirmed by numerical experiments, shows that the achieved speedup can be well over 100.
PB Springer Nature
SN 0885-7474
YR 2016
FD 2016-02
LK https://hdl.handle.net/10016/32112
UL https://hdl.handle.net/10016/32112
LA eng
NO This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) under grants UID/CEC/50021/2013, and PTDC/EIA-CCO/098910/2008. FB also acknowledges FCT funding under grant SFRH/BPD/79986/2011.
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RD 1 sept. 2024