Adaptive quadrature - Revisited
Adaptive quadrature - Revisited
复制标题
DOI：
10.1023/a:1022318402393
复制
发表时间：
2000-01-01
期刊：
影响因子：
1.5
通讯作者：
Gautschi, W
中科院分区：
文献类型：
--
作者：
Gander, W;Gautschi, W
首先，回顾了自适应求积的基本原理。自适应正交程序是递归的性质，一个良好的终止标准的选择给予特别注意。给出了两个Matlab求积程序。第一个是著名的自适应递归辛普森规则的实现;第二个是新的，是基于四点高斯-洛巴托公式和两个连续的克朗罗德扩展。比较测试结果的描述和注意的严重缺陷，由Matlab提供的自适应例程四和quad 8。
First, the basic principles of adaptive quadrature are reviewed. Adaptive quadrature programs being recursive by nature, the choice of a good termination criterion is given particular attention. Two Matlab quadrature programs are presented. The rst is an implementation of the well-known adaptive recursive Simpson rule; the second is new and is based on a four-point Gauss-Lobatto formula and two successive Kronrod extensions. Comparative test results are described and attention is drawn to serious deficiencies in the adaptive routines quad and quad8 provided by Matlab.