具有超强收敛性的多维立体公式

IF 0.5 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2024-03-14 DOI:10.1134/S1064562423701478

A. A. Belov, M. A. Tintul

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引用次数: 0

摘要

在许多应用中，都会出现单位超立方体上的多维积分，这些积分是用蒙特卡罗方法计算的。其中最好的方法收敛速度相当慢。本文基于改进的 Korobov 网格和特殊的变量替换，提出了具有超强收敛性的全新立方公式。本文构建的后验误差估计值与实际精度几乎没有差别。计算实例说明了所提方法的优势。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Multidimensional Cubature Formulas with Superpower Convergence

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Multidimensional Cubature Formulas with Superpower Convergence

In many applications, multidimensional integrals over the unit hypercube arise, which are calculated using Monte Carlo methods. The convergence of the best of them turns out to be quite slow. In this paper, fundamentally new cubature formulas with superpower convergence based on improved Korobov grids and a special variable substitution are proposed. A posteriori error estimates are constructed, which are nearly indistinguishable from the actual accuracy. Examples of calculations illustrating the advantages of the proposed methods are given.

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来源期刊

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.