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Mancini, S., Bernal, F. & Acebron, J. A. (2016). An efficient algorithm for accelerating Monte Carlo approximations of the solution to boundary value problems. Journal of Scientific Computing. 66 (2), 577-597
S. Mancini et al., "An efficient algorithm for accelerating Monte Carlo approximations of the solution to boundary value problems", in Journal of Scientific Computing, vol. 66, no. 2, pp. 577-597, 2016
@article{mancini2016_1714796486190, author = "Mancini, S. and Bernal, F. and Acebron, J. A.", title = "An efficient algorithm for accelerating Monte Carlo approximations of the solution to boundary value problems", journal = "Journal of Scientific Computing", year = "2016", volume = "66", number = "2", doi = "10.1007/s10915-015-0033-4", pages = "577-597", url = "http://link.springer.com/article/10.1007%2Fs10915-015-0033-4" }
TY - JOUR TI - An efficient algorithm for accelerating Monte Carlo approximations of the solution to boundary value problems T2 - Journal of Scientific Computing VL - 66 IS - 2 AU - Mancini, S. AU - Bernal, F. AU - Acebron, J. A. PY - 2016 SP - 577-597 SN - 0885-7474 DO - 10.1007/s10915-015-0033-4 UR - http://link.springer.com/article/10.1007%2Fs10915-015-0033-4 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. ER -