Construction of \(\sigma\)-orthogonal polynomials and Gaussian quadrature formulas

DOI10.1007/s10444-007-9033-8zbMath1122.65026OpenAlexW1974211802MaRDI QIDQ996796

Ying Guang Shi, Guo-liang Xu

Publication date: 19 July 2007

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-007-9033-8

zbMATH Keywords

algorithmnumerical examplesCotes numbersGaussian quadrature formulasgeneralized orthogonal polynomials

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Computation of special functions and constants, construction of tables (65D20) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items (13)

Estimating the error of Gaussian quadratures with simple and multiple nodes by using their extensions with multiple nodes ⋮ Error estimations of Turán formulas with Gori-Micchelli and generalized Chebyshev weight functions ⋮ Quadrature Rules with Multiple Nodes ⋮ Convergence of Gaussian quadrature formulas on infinite intervals ⋮ Error estimates of Gaussian-type quadrature formulae for analytic functions on ellipses -- survey of recent results ⋮ Kronrod extensions with multiple nodes of quadrature formulas for Fourier coefficients ⋮ Best quadrature formula on Sobolev class with Chebyshev weight ⋮ Bounds of the error of Gauss-Turán-type quadratures. II. ⋮ High-precision Gauss-Turán quadrature rules for Laguerre and Hermite weight functions ⋮ The Remainder Term of Gauss–Turán Quadratures for Analytic Functions ⋮ Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness ⋮ Christoffel type functions for \(m\)-orthogonal polynomials ⋮ A uniqueness theorem of a system of nonlinear equations and its applications

Cites Work

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• Generalized Gaussian quadrature formulas
• On some problems of P. Turán concerning \(L_m\) extremal polynomials and quadrature formulas
• \(S\)-orthogonality and construction of Gauss-Turán-type quadrature formulae
• On Hermite interpolation
• Quadrature formulae connected to sigma-orthogonal polynomials
• On Multiple Node Gaussian Quadrature Formulae
• Quadratures with multiple nodes, power orthogonality, and moment-preserving spline approximation

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