Faster Evaluation of Multidimensional Integrals

作者：Anargyros Papageorgiou, Joseph F. Traub · 发表于：Computers in Physics · 年份：1997 · DOI：10.1063/1.168616 · 被引用次数：78 · 研究领域：Iterative Methods for Nonlinear Equations、Numerical Methods and Algorithms、Matrix Theory and Algorithms

In a recent paper Keister proposed two quadrature rules as alternatives to Monte Carlo for certain multidimensional integrals and reported his test results. In earlier work we had shown that the quasi-Monte Carlo method with generalized Faure points is very effective for a variety of high dimensional integrals occurng in mathematical finance. In this paper we report test results of this method on Keister's examples of dimension 9 and 25, and also for examples of dimension 60, 80 and 100. For the 25 dimensional integral we achieved accuracy of 0.01 with less than 500 points while the two methods tested by Keister used more than 220,000 points. In all of our tests, for n sample points we obtained an empirical convergence rate proportional to n^{-1} rather than the n^{-1/2} of Monte Carlo.