Gaussian, Lobatto and Radau positive quadrature rules with a prescribed abscissa

DOI10.1007/s10092-013-0087-3zbMath1312.65032OpenAlexW2151818338MaRDI QIDQ2017989

Reinaldo Martínez-Cruz, Bernhard Beckermann, José María Quesada, Jorge Bustamante González

Publication date: 23 March 2015

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10092-013-0087-3

zbMATH Keywords

degree of precisionquasi-orthogonal polynomialspositive quadrature formulaGauss ruleLobatto ruleprescribed abscissaRadau rule

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

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One-sided integral approximation of the characteristic function of an interval by algebraic polynomials ⋮ Low-Order Preconditioning for the High-Order Finite Element de Rham Complex ⋮ Zeros of quasi-orthogonal ultraspherical polynomials ⋮ Quadrature rules for \(L^1\)-weighted norms of orthogonal polynomials ⋮ One-sided weighted integral approximation of characteristic functions of intervals by polynomials on a closed interval ⋮ Best one-sided approximation in the mean of the characteristic function of an interval by algebraic polynomials ⋮ ONE-SIDED L-APPROXIMATION ON A SPHERE OF THE CHARACTERISTIC FUNCTION OF A LAYER ⋮ Erratum to: ``On Gauss-type quadrature formulas with prescribed nodes anywhere on the real line ⋮ On spherical codes with inner products in a prescribed interval ⋮ Quasi-orthogonality of some hypergeometric polynomials ⋮ Universal lower bounds for potential energy of spherical codes ⋮ Quasi orthogonal Jacobi polynomials and best one-sided \(L_1\) approximation to step functions ⋮ Zeros of quasi-paraorthogonal polynomials and positive quadrature ⋮ A connection between Szegő-Lobatto and quasi Gauss-type quadrature formulas ⋮ Radau and Lobatto-type quadratures associated with strong Stieltjes distributions

Cites Work

• Best one-sided \(L_1\) approximation to the Heaviside and sign functions
• Interlacing of the zeros of Jacobi polynomials with different parameters
• Quasi-orthogonality with applications to some families of classical orthogonal polynomials.
• On Gauss-type quadrature formulas with prescribed nodes anywhere on the real line
• Linear Combinations of Orthogonal Polynomials Generating Positive Quadrature Formulas
• Unnamed Item

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