Gauss quadrature routines for two classes of logarithmic weight functions

被引：17

作者：

Gautschi, Walter ^{[1
]}

机构：

[1] Purdue Univ, Dept Comp Sci, W Lafayette, IN 47907 USA

来源：

NUMERICAL ALGORITHMS | 2010年 / 55卷 / 2-3期

关键词：

Gaussian quadrature; Logarithmic weight functions; Orthogonal polynomials; Modified Chebyshev algorithm; Variable-precision arithmetic;

D O I：

10.1007/s11075-010-9366-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By means of the Matlab symbolic/variable-precision facilities, routines are developed that generate an arbitrary number of recurrence coefficients to any given precision for polynomials orthogonal with respect to weight functions of Laguerre and Jacobi type containing logarithmic factors. The vehicle used is a symbolic modified Chebyshev algorithm based on ordinary as well as modified moments, executed with sufficiently high precision. The results are applied to Gaussian quadrature of integrals involving weight functions of the type mentioned.

引用

页码：265 / 277

页数：13

共 21 条

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