FAST AND ACCURATE COMPUTATION OF GAUSS-LEGENDRE AND GAUSS-JACOBI QUADRATURE NODES AND WEIGHTS

被引：130
|
作者：
Hale, Nicholas [1 ]
Townsend, Alex [1 ]
机构：
[1] Math Inst, Oxford OX1 3LB, England
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2013年 / 35卷 / 02期
关键词：
quadrature; Gauss-Legendre; Gauss-Jacobi; asymptotic expansion; CONVERGENCE-RATES; FAST ALGORITHM; POLYNOMIALS; ZEROS; APPROXIMATIONS; ASYMPTOTICS; SERIES;
D O I：
10.1137/120889873
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An efficient algorithm for the accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights is presented. The algorithm is based on Newton's root-finding method with initial guesses and function evaluations computed via asymptotic formulae. The n-point quadrature rule is computed in O(n) operations to an accuracy of essentially double precision for any n >= 100.
引用
收藏
页码：A652 / A674
页数：23
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