Exactness of quadrature formulas

IF 10.8 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Review Pub Date : 2021-01-23 DOI:10.1137/20m1389522

L. Trefethen

引用次数: 26

Abstract

The standard design principle for quadrature formulas is that they should be exact for integrands of a given class, such as polynomials of a fixed degree. We show how this principle fails to predict the actual behavior in four cases: Newton–Cotes, Clenshaw–Curtis, Gauss–Legendre, and Gauss–Hermite quadrature. Three further examples are mentioned more briefly.

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求积分公式的准确性

正交公式的标准设计原则是，对于给定类别的被积函数，如固定次多项式，它们应该是精确的。我们展示了这个原理在四种情况下是如何无法预测实际行为的:牛顿-柯茨、克伦肖-柯蒂斯、高斯-勒让德和高斯-埃尔米特正交。还有三个更简单的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Review 数学-应用数学

CiteScore

16.90

自引率

0.00%

发文量

期刊介绍： Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter. Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.