期刊
SIAM REVIEW
卷 50, 期 1, 页码 67-87出版社
SIAM PUBLICATIONS
DOI: 10.1137/060659831
关键词
Gauss quadrature; Newton-Cotes; Clenshaw-Curtis; Chebyshev expansion; rational approxiination; FFT; spectral methods
We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw-Curtis. Seven-line MATLAB codes are presented that implement both methods, and experiments show that the supposed factor-of-2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following O'Hara and Smith in the 1960s, the phenomenon is explained as a consequence of aliasing of coefficients in Chebyshev expansions. Then another explanation is offered based on the interpretation of a quadrature formula as a, rational approximation of log((z + 1)/(z - 1)) in the complex plane. Gauss quadrature corresponds to Pade approximation at z = infinity. Clenshaw-Curtis quadrature corresponds to an approximation whose order of accuracy at z = infinity is only half as high, but which is nevertheless equally accurate near [-1, 1].
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据