On the approximate calculation of multiple integrals

被引：41

作者：

Bakhvalov, Nikolai Sergeevich ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Dept Computat Math, Moscow, Russia

来源：

JOURNAL OF COMPLEXITY | 2015年 / 31卷 / 04期

关键词：

Optimal quadrature formulas; Monte Carlo methods;

D O I：

10.1016/j.jco.2014.12.003

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

When approximately calculating integrals of high dimension with the Monte Carlo method, one uses fewer values of the integrand than when calculating with the help of classical deterministic quadrature formulas. However, the error estimation for the Monte Carlo method does not depend on the smoothness of the integrand. This suggests that it is possible to obtain methods that give a better order of convergence in case of smooth functions. (C) 2015 Published by Elsevier Inc.

引用

页码：502 / 516

页数：15

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