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

[1] Gauss quadrature routines for two classes of logarithmic weight functions
Walter Gautschi
Numerical Algorithms, 2010, 55 : 265 - 277
[2] Algorithm 867: QUADLOG - A package of routines for generating Gauss-related quadrature for two classes of logarithmic weight functions
Beebe, Nelson H. F.
Ball, James S.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2007, 33 (03): : D1 - D30
[3] Efficient Gauss-related quadrature for two classes of logarithmic weight functions
Ball, James S.
Beebe, Nelson H. F.
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2007, 33 (03): : C1 - C21
[4] The error norm of Gauss-Radau quadrature formulae for Chebyshev weight functions
Notaris, Sotirios E.
BIT NUMERICAL MATHEMATICS, 2010, 50 (01) : 123 - 147
[5] Orthogonal polynomials and Gaussian quadrature for refinable weight functions
Laurie, DP
de Villiers, JM
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2004, 17 (03) : 241 - 258
[6] GAUSS-KRONROD QUADRATURE-FORMULAS FOR WEIGHT-FUNCTIONS OF BERNSTEIN-SZEGO TYPE .2.
NOTARIS, SE
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1990, 29 (02) : 161 - 169
[7] Orthogonal polynomials and Gaussian quadrature rules related to oscillatory weight functions
Milovanovic, GV
Cvetkovic, AS
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 179 (1-2) : 263 - 287
[8] Remark on Algorithm 726: ORTHPOL - A package of routines for generating orthogonal polynomials and Gauss-type quadrature rules
Gautschi, W
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1998, 24 (03): : 355 - 357
[9] CONSTRUCTION OF GAUSSIAN QUADRATURE FORMULAS FOR EVEN WEIGHT FUNCTIONS
Masjed-Jamei, Mohammad
Milovanovic, Gradimir V.
APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2017, 11 (01) : 177 - 198
[10] ALGORITHM-726 - ORTHPOL - A PACKAGE OF ROUTINES FOR GENERATING ORTHOGONAL POLYNOMIALS AND GAUSS-TYPE QUADRATURE-RULES
GAUTSCHI, W
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 1994, 20 (01): : 21 - 62

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