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- W2145604916 abstract "In this paper we present and analyze a quasi-Monte Carlo method for solving elliptic boundary value problems. Our method transforms the given partial differential equation into an integral equation by employing a well known local integral representation. The kernel in this integral equation representation can be used as a transition density function to define a Markov process used in estimating the solution. The particular process, called a random walk on balls process, is subsequently generated using quasirandom numbers. Two approaches of using quasirandom numbers for this problem, which uses an acceptance-rejection method to compute the transition probabilities, are presented. We also estimate the accuracy and the computational complexity of the quasi-Monte Carlo method. Finally, results from numerical experiments with Sobol and Halton quasirandom sequences are presented and are compared to the results with pseudorandom numbers. The results with quasirandom numbers provide a slight improvement over regular Monte Carlo methods. We believe that both the relatively high effective dimension of this problem and the use of the acceptance-rejection method impede significant convergence acceleration often seen with some quasi-Monte Carlo methods." @default.
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- W2145604916 date "2001-01-01" @default.
- W2145604916 modified "2023-10-17" @default.
- W2145604916 title "A Quasi-Monte Carlo Method for Elliptic Boundary Value Problems" @default.
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- W2145604916 doi "https://doi.org/10.1515/mcma.2001.7.3-4.283" @default.
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