A Review of Error Estimation in Adaptive Quadrature

被引：31
作者：
Gonnet, Pedro [1 ,2 ]
机构：
[1] ETH, Zurich, Switzerland
[2] Univ Oxford, Oxford OX1 2JD, England
来源：
ACM COMPUTING SURVEYS | 2012年 / 44卷 / 04期
关键词：
Algorithms; Reliability; Numerical integration; adaptive quadrature; error estimation; DEFINITE INTEGRALS; ALGORITHM; ROUTINES; SYSTEMS;
D O I：
10.1145/2333112.2333117
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated, and discussed. This article presents a review of existing error estimation techniques and discusses their differences and their common features. Some common shortcomings of these algorithms are discussed, and a new general error estimation technique is presented.
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页数：36
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