Gauss quadrature routines for two classes of logarithmic weight functions

DOI10.1007/s11075-010-9366-0zbMath1200.65019OpenAlexW1967194308MaRDI QIDQ1960242

Walter Gautschi

Publication date: 13 October 2010

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-010-9366-0

zbMATH Keywords

orthogonal polynomialsGaussian quadraturevariable-precision arithmeticmodified Chebyshev algorithmlogarithmic weight functions

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Quantization of the gravitational field (83C45) Computation of special functions and constants, construction of tables (65D20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (13)

A method for efficient computation of integrals with oscillatory and singular integrand ⋮ A new triangular spectral element method. I: Implementation and analysis on a triangle ⋮ Efficient methods for highly oscillatory integrals with weak and Cauchy singularities ⋮ Efficient numerical methods for hypersingular finite-part integrals with highly oscillatory integrands ⋮ Gaussian integration formulas for logarithmic weights and application to 2-dimensional solid-state lattices ⋮ Unnamed Item ⋮ Efficient quadrature rules for the singularly oscillatory Bessel transforms and their error analysis ⋮ Efficient computation of highly oscillatory integrals with weak singularities by Gauss-type method ⋮ Efficient method for the computation of oscillatory Bessel transform and Bessel Hilbert transform ⋮ GQLOG ⋮ The modified composite Gauss type rules for singular integrals using Puiseux expansions ⋮ Efficient numerical methods for Cauchy principal value integrals with highly oscillatory integrands ⋮ On the rational Levin quadrature for evaluation of highly oscillatory integrals and its application

Uses Software

• Matlab
• ORTHPOL
• OPQ

Cites Work

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• High-order generalized Gauss-Radau and Gauss-Lobatto formulae for Jacobi and Laguerre weight functions
• Efficient Gauss-related quadrature for two classes of logarithmic weight functions
• On Some Orthogonal Polynomial Integrals
• Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules

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