Alternation theory in approximation by polynomials having bounded coefficients
type: Item
instance of: scholarly article
title: Alternation theory in approximation by polynomials having bounded coefficients
zbMATH Open document ID: 0823.41024
DOI: 10.1007/BF02006857
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1995-11-06T00:00:00Z
review text: Let \(X\) be a compact subset of an interval \([a, b]\), where \(ab\geq 0\), \(f\) a continuous function defined on \(X\) and \[ K= \Biggl\{ p= \sum^ n_{j= 0} a_ j x^ j\mid \alpha_ j\leq a_ j\leq \beta_ j,\;j= 0,\dots,n\Biggr\} \] the set of algebraic polynomials having bounded coefficients. In this paper the author points out an alternating characterization theorem of a polynomial of best uniform approximation to \(f\) from \(K\), and de la Vallée-Poussin theorem.
reviewed by: Silvestru Sever Dragomir
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 713757
zbMATH Keywords: alternation theory
zbMATH Keywords: best approximation
author: Shusheng Xu
MaRDI profile type: Publication
cites work: Strong uniqueness of generalized polynomial of best approximation having bounded coefficients
cites work: Q5650526
cites work: Characterization theorem of generalized polynomial of best approximation having bounded coefficients
cites work: Q5543516
description: scientific article; zbMATH DE number 713757