On Gaussian quadrature formulas for the Chebyshev weight
type: Item
instance of: scholarly article
title: On Gaussian quadrature formulas for the Chebyshev weight
zbMATH Open document ID: 0921.41013
author: Yingguang Shi
published in: Journal of Approximation Theory
publication date: 1999-05-17T00:00:00Z
review text: The names of Gauss and Chebyshev, great and illustrious as they are, appear in the mathematics literature quite a good number of times. Particularly, Chebyshev polynomials and Gaussian quadrature are well-known independently and to connect them up in a meaningful manner is a task worthy of note. In the paper under review the author has studied in depth and shown that the Chebyshev weight \(W(x)= (1-x^2)^{-1/2}\) is the only one possessing the property (up to a linear transformation) that the solutions of a specific extremal problem are identical for any values of two parameters \((m,p\geq 1)\). The special conditions required for this are characterized through two theorems with detailed proof, a remark and five auxiliary lemmas, three of which are followed by brief justification also. As a generalization of the earlier research results by the same author, the present contribution is an important addition to certain approximation theories and their applications.
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 1288058
zbMATH Keywords: Gaussian quadrature
MaRDI profile type: Publication
full work available at URL: jath.1998.3284
OpenAlex ID: W4213138769
cites work: Q3969325
cites work: Generalized Gaussian quadrature formulas
cites work: Q5543516
cites work: General Gaussian quadrature formulas on Chebyshev nodes.
DOI: 10.1006/JATH.1998.3284
description: scientific article; zbMATH DE number 1288058