Alternation points, weights and orthogonal polynomials

DOI10.1016/j.jat.2022.105834OpenAlexW4306974848MaRDI QIDQ2104955

Lawrence A. Harris

Publication date: 8 December 2022

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2022.105834

zbMATH Keywords

discrete inner productChebyshev polynomialJacobi polynomialgenerating weightsgeronimus polynomial

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Quadratic and bilinear forms, inner products (15A63) Harmonic analysis on Euclidean spaces (42-XX) Approximations and expansions (41-XX)

Uses Software

• OPQ

Cites Work

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• Alternation points and bivariate Lagrange interpolation
• Lagrange polynomials, reproducing kernels and cubature in two dimensions
• A characterization of the four Chebyshev orthogonal families
• Fast and Stable Rational Interpolation in Roots of Unity and Chebyshev Points
• Bivariate Polynomial Interpolation at the Geronimus Nodes
• Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials
• Discrete orthogonal polynomials on equidistant nodes
• Interpolation and cubature for rectangular sets of nodes
• Bivariate Lagrange interpolation at the checkerboard nodes
• On the ``Favard theorem and its extensions

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