An Efficient Algorithm for Accelerating Monte Carlo Approximations of the Solution to Boundary Value Problems
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 Mon...
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| Veröffentlicht in: | Journal of scientific computing 2016-02, Vol.66 (2), p.577-597 |
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| container_title | Journal of scientific computing |
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| creator | Mancini, Sara Bernal, Francisco Acebrón, Juan A. |
| description | 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. |
| doi_str_mv | 10.1007/s10915-015-0033-4 |
| format | Article |
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| ispartof | Journal of scientific computing, 2016-02, Vol.66 (2), p.577-597 |
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| language | eng |
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| source | SpringerNature Journals; ProQuest Central UK/Ireland; ProQuest Central |
| subjects | Accuracy Algorithms Approximation Bias Boundary value problems Clouds Computational Mathematics and Numerical Analysis Estimates Expected values Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical models Mathematics Mathematics and Statistics Monte Carlo methods Monte Carlo simulation Partial differential equations Simulation Statistical analysis Theoretical |
| title | An Efficient Algorithm for Accelerating Monte Carlo Approximations of the Solution to Boundary Value Problems |
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