The Diliberto-Straus algorithm in \(L_ 1(X\times Y)\)
type: Item
instance of: scholarly article
title: The Diliberto-Straus algorithm in \(L_ 1(X\times Y)\)
zbMATH Open document ID: 0536.41029
DOI: 10.1016/0021-9045(83)90137-5
author: W. A. Light
published in: Journal of Approximation Theory
publication date: 1983-01-01T00:00:00Z
review text: The Diliberto-Straus algorithm is already a familiar tool for producing best approximations to bivariate functions in \(C(S\times T)\) by sums of univariate functions in \(C(S)+C(T)\). This paper investigates the performance of the algorithm in the space \(C(S\times T)\) with the \(L_ 1\)-norm. In this case there are already examples where the algorithm is known not to converge but this paper shows that under certain mild hypotheses (equivalent to the initial function being smooth with respect to the subspace) the norms of the elements in the algorithm converge to the distance from the initial function to the subspace \(C(S)+C(T)\) in the \(L_ 1\)-norm.
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 3851677
zbMATH Keywords: Diliberto-Straus algorithm
zbMATH Keywords: bivariate functions
MaRDI profile type: Publication
full work available at URL: 0021-9045(83)90137-5
OpenAlex ID: W2054076318
cites work: Q3289358
cites work: The approximation of bivariate functions by sums of univariate ones using the L1-metric
cites work: On the approximation of a function of several variables by the sum of functions of fewer variables
cites work: Orthogonality and Linear Functionals in Normed Linear Spaces
description: scientific article; zbMATH DE number 3851677