Discrete orthogonal polynomials on Gauss-Lobatto Chebyshev nodes
type: Item
instance of: scholarly article
title: Discrete orthogonal polynomials on Gauss-Lobatto Chebyshev nodes
zbMATH Open document ID: 1117.65040
published in: Journal of Approximation Theory
publication date: 2007-02-26T00:00:00Z
review text: This paper deals with explicit formulas for discrete orthogonal polynomials over the so-called Gauss-Lobatto Chebyshev nodes \[ X_n=\{x_k=-\cos((k-1)\pi/(n-1))\},\quad k=1, 2, \ldots ,n. \] The orthogonal polynomials \(p_k(x)\) (\(k=1, 2, \dots ,n\)) with respect to the discrete inner product \(\langle f,g\rangle=\sum_{k=1}^nf(x_k)g(x_k)\) on the set \(X_n\) can be related to the Chebyshev polynomials of the first and second kinds. The authors derive explicit expressions of these polynomials and obtain the coefficients in the 3-term recurrence relation that they satisfy. They also obtain formulas for the discrete inner product \(\langle p_k, p_k\rangle\) (\(k=1, 2, \dots , n\)). Numerical examples related to least-squares problems are also given.
reviewed by: Richard B. Paris
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33F05
zbMATH DE Number: 5129687
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: least-squares
zbMATH Keywords: hypergeometric functions
zbMATH Keywords: 3-term recurrence relation
zbMATH Keywords: numerical examples
zbMATH Keywords: least-squares problems
author: A. Eisinberg
author: Giuseppe Fedele
describes a project that uses: Mathematica
describes a project that uses: OPQ
MaRDI profile type: Publication
full work available at URL: j.jat.2006.06.003
OpenAlex ID: W2162140727
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DOI: 10.1016/J.JAT.2006.06.003
description: scientific article; zbMATH DE number 5129687