Multiple-precision correctly rounded newton-cotes quadrature

被引：2

作者：

Fousse, Laurent ^{[1
]}

机构：

[1] Univ Nancy 1, LORIA, F-54602 Villers Les Nancy, France

来源：

RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS | 2007年 / 41卷 / 01期

关键词：

numerical integration; correct rounding; multiple-precision; Newton-Cotes;

D O I：

10.1051/ita:2007004

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Numerical integration is an important operation for scientific computations. Although the different quadrature methods have been well studied from a mathematical point of view, the analysis of the actual error when performing the quadrature on a computer is often neglected. This step is however required for certified arithmetics. We study the Newton-Cotes quadrature scheme in the context of multiple-precision arithmetic and give enough details on the algorithms and the error bounds to enable software developers to write a Newton-Cotes quadrature with bounded error.

引用

页码：103 / 121

页数：19

共 50 条

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