A note on a result of Bernstein
type: Item
instance of: scholarly article
title: A note on a result of Bernstein
zbMATH Open document ID: 0626.41004
DOI: 10.1016/0021-9045(86)90023-7
author: Jianyong Qiao
author: Sumit K. Garg
published in: Journal of Approximation Theory
publication date: 1986-01-01T00:00:00Z
review text: The author proves that for any \(a\geq 2\), the function \((1-x)^{-1}\) can be approximated on [-1/a,1/a] by polynomials of degree n, having nonnegative, nonincreasing coefficients with an error \(<a(a^{n+1}- 1)^{-1}\); but never better than \((a^{n+1}-1)^{-1}\). It is also proved that the smallest maximal error in a uniform approximation of 1-x on [0,1] by ratios of polynomials of degree \(\leq n\), \(n\geq 0\), having nonnegative, nonincreasing coefficients is \((n+2)^{-1}\).
reviewed by: László Leindler
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 4017531
zbMATH Keywords: maximal error
zbMATH Keywords: uniform approximation
MaRDI profile type: Publication
full work available at URL: 0021-9045(86)90023-7
OpenAlex ID: W2093681568
cites work: Q5727762
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description: scientific article; zbMATH DE number 4017531