Orthogonal polynomials and Gaussian quadrature rules related to oscillatory weight functions

DOI10.1016/j.cam.2004.09.044zbMath1074.41026OpenAlexW1992186768WikidataQ115058793 ScholiaQ115058793MaRDI QIDQ1779447

Gradimir V. Milovanović, Aleksandar S. Cvetković

Publication date: 1 June 2005

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.09.044

zbMATH Keywords

Orthogonal polynomialsGaussian quadratureMomentsOscillatory weight functionThree-term recurrence relationZero distribution

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Approximate quadratures (41A55)

Related Items (4)

Numerical Integration of Highly Oscillating Functions ⋮ Gaussian type quadrature rules related to the oscillatory modification of the generalized Laguerre weight functions ⋮ The Scientific Work of Gradimir V. Milovanović ⋮ Orthogonal polynomials for modified Gegenbauer weight and corresponding quadratures

Uses Software

• OrthogonalPolynomials
• ORTHPOL

Cites Work

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• A generalization of Poincaré's theorem for recurrence equations
• Polynomials orthogonal on a circular arc
• Polynomials orthogonal on the semicircle
• Toeplitz matrix techniques and convergence of complex weight Padé approximants
• Polynomials orthogonal on the semicircle. II
• Numerical calculation of integrals involving oscillatory and singular kernels and some applications of quadratures
• Spurious poles in Padé approximation
• On polynomials orthogonal on a circular arc
• Accurate computation of the zeros of the generalized Bessel polynomials
• On the convergence of quadrature formulas for complex weight functions
• Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
• Gaussian Integration for Complex Weight Functions
• Algorithm 726: ORTHPOL–a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules
• Complex Jacobi matrices and quadrature rules
• Calculation of Gauss Quadrature Rules

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