Fast convergence of quasi-Monte Carlo for a class of isotropic integrals期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Fast convergence of quasi-Monte Carlo for a class of isotropic integrals

Authors:	A Papageorgiou

Institution:	Department of Computer Science, Columbia University, New York, NY 10027

Abstract:	We consider the approximation of -dimensional weighted integrals of certain isotropic functions. We are mainly interested in cases where is large. We show that the convergence rate of quasi-Monte Carlo for the approximation of these integrals is $O(\sqrt{\log n}/n)$ . Since this is a worst case result, compared to the expected convergence rate $O(n^{-1/2})$ of Monte Carlo, it shows the superiority of quasi-Monte Carlo for this type of integral. This is much faster than the worst case convergence, $O(\log^d n/n)$ , of quasi-Monte Carlo.

Keywords:	Multidimensional integration quadrature Monte Carlo methods low discrepancy sequences quasi-Monte Carlo methods

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