Convergence properties of a quadrature formula of Clenshaw-Curtis type for the Gegenbauer weight function

被引：0
|
作者：
Smith, H. V. [1 ]
机构：
[1] Quadrature Res Ctr, Dumfries DG2 9RA, Scotland
来源：
BIT NUMERICAL MATHEMATICS | 2015年 / 55卷 / 03期
关键词：
Gegenbauer weight function; Clenshaw-Curtis quadrature; Convergence rate; Lobatto-Chebyshev quadrature;
D O I：
10.1007/s10543-014-0520-2
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
A quadrature formula of Clenshaw-Curtis type for functions of the form (1-x(2))(lambda-1/2) f(x) over the interval [-1,1] exhibits a curious phenomenon when applied to certain analytic functions. As the number of points in the quadrature rule increases the error may sometimes decay to zero in two distinct stages rather than in one depending on the value of lambda. In this paper we shall derive explicit and asymptotic error formulae which describe this phenomenon.
引用
收藏
页码：823 / 842
页数：20
相关论文
共 50 条
12345