The Polya algorithm in \(L_{\infty}\) approximation
type: Item
instance of: scholarly article
title: The Polya algorithm in \(L_{\infty}\) approximation
zbMATH Open document ID: 0533.41036
DOI: 10.1016/0021-9045(83)90129-6
published in: Journal of Approximation Theory
publication date: 1983-01-01T00:00:00Z
review text: Two aspects of the Polya algorithm are considered - (a) the monotone approximation in \(L_{\infty}(I)\) and (b) approximating functions in \(L_{\infty}(\Omega,{\mathcal A},\mu;x)\) by functions in \(L_{\infty}(\Omega,{\mathcal B},\mu;x)\) where \({\mathcal B}\) is sub \(\sigma\)- algebra of \({\mathcal A}\) and x is a uniformly convex Banach space. It is shown (a) how the Polya algorithm fails to converge for \(h\in L_{\infty}(I)\) and (b) how to find the best best \(L_{\infty}\) approximation to f.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 3846163
zbMATH Keywords: Polya algorithm
zbMATH Keywords: monotone approximation
zbMATH Keywords: approximating functions
author: Richard B. Darst
author: David A. Legg
author: Douglas W. Townsend
reviewed by: S. K. Rangarajan
MaRDI profile type: Publication
full work available at URL: 0021-9045(83)90129-6
OpenAlex ID: W2046335995
description: scientific article; zbMATH DE number 3846163