Best one-sided \(L_1\) approximation to the Heaviside and sign functions
type: Item
instance of: scholarly article
title: Best one-sided \(L_1\) approximation to the Heaviside and sign functions
zbMATH Open document ID: 1248.41013
author: Reinaldo Martínez-Cruz
author: Jorge Bustamante
author: José M. Quesada
published in: Journal of Approximation Theory
publication date: 2012-07-11T00:00:00Z
review text: An explicit expression for polynomials of best one-sided approximation to the Heaviside function~\(G\) (and hence to the sign function) is obtained. Characterization of the polynomials in \(\mathcal P^{-1}(G)\) is established. The polynomials are obtained by Hermite interpolation at the zeros of some Jacobi polynomials. An estimate of the error of approximation is given, and the extreme points of the convex set of the best approximants are characterized.
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 6054348
zbMATH Keywords: one-sided approximation
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: Hermite interpolation
reviewed by: A. R. Alimov
MaRDI profile type: Publication
full work available at URL: j.jat.2012.02.006
OpenAlex ID: W2089540934
cites work: On polynomials of best one sided approximation
cites work: Best one-sided approximation of polynomials under \({\mathbf L}_1\) norm
cites work: One-sided approximation of a step by algebraic polynomials in the mean
cites work: Q3994890
DOI: 10.1016/J.JAT.2012.02.006
description: scientific article; zbMATH DE number 6054348