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

被引：138

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

页码：A652 / A674

页数：23

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