The Exact Degree of Precision of Generalized Gauss-Kronrod Integration Rules

DOI10.2307/2006392zbMath0461.65019OpenAlexW4241444103MaRDI QIDQ3911273

Philip Rabinowitz

Publication date: 1980

Full work available at URL: https://doi.org/10.2307/2006392

zbMATH Keywords

Gegenbauer polynomialsSzegö polynomialsFourier coefficientsLobatto integration ruleKronrod ruleGauss integration rule

Mathematics Subject Classification ID

Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items

Error bounds for Gauss-Kronrod quadrature formulae of analytic functions ⋮ The work of Philip Rabinowitz on numerical integration ⋮ Quadrature formulas for Fourier coefficients ⋮ Extended product integration rules ⋮ Asymptotic behaviour of Stieltjes polynomials for ultraspherical weight functions ⋮ Unnamed Item ⋮ Error Bounds for Gauss-Kronrod Quadrature Formulae ⋮ Stopping functionals for Gaussian quadrature formulas ⋮ Computation of nodes and weights of extended Gaussian rules

Cites Work

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• Nonexistence of extended Gauss-Laguerre and Gauss-Hermite quadrature rules with positive weights
• A Note on Extended Gaussian Quadrature Rule
• Positivity of the Weights of Extended Gauss-Legendre Quadrature Rules
• Some Remarks on the Construction of Extended Gaussian Quadrature Rules
• A Note on the Optimal Addition of Abscissas to Quadrature Formulas of Gauss and Lobatto Type
• Turán Formulae and Highest Precision Quadrature Rules for Chebyshev Coefficients
• The Optimum Addition of Points to Quadrature Formulae