Errata Corrige: ''Two extensions of the alternating algorithm of von Neumann''
type: Item
instance of: scholarly article
title: Errata Corrige: ''Two extensions of the alternating algorithm of von Neumann''
zbMATH Open document ID: 0549.41021
DOI: 10.1007/BF01766864
author: S. M. Holland
author: Carlo Franchetti
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1985-01-01T00:00:00Z
review text: In Theorems 1 and 2 the assumption that \(U+V\) is a linear subspace cannot be omitted. In fact, the given proof relies on the fact that \(J_{2n}(w- w_ n)\leq\sigma_ n(\sigma_ n\to 0)\) which does not follow from the established inequalities \(J_{2n}(w)\leq\epsilon_ n\), \(J_{2n}(w_ n)\leq\epsilon_ n (\epsilon_ n\to 0)\). However, if \(U+V\) is a linear subspace, since \((w-w_ n)\in U+V\) it can be shown that \(J_{2n}(w-w_ n)\leq\epsilon_ n\) the same way that it was for \(J_{2n}(w)\) or \(J_{2n}(w_ n)\). It is a very regrettable fact that Lemma 5 ii) and Theorem 3 respectively have an incorrect proof and no proof at all so that Theorem 4 need not be true.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41A50
zbMATH DE Number: 3875931
zbMATH Keywords: closed wedges
zbMATH Keywords: von Neumann theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01766864
OpenAlex ID: W2020040198
Recommended article: Two extensions of the alternating algorithm of von Neumann
Recommended article: Erratum: On Regularity Lemmas and their Algorithmic Applications
Recommended article: Corrigendum to: ``An algorithm for computing all Berge equilibria''
Recommended article: Erratum to: ``Algorithms for solutions of extended general mixed variational inequalities and fixed points''
Recommended article: Erratum to: ``The convergence of the generalised Selmer algorithm''
Recommended article: Erratum: A correction to ''Parallel approximation algorithms by positive linear programming''
Recommended article: Erratum to: ``Algorithms for the orthographic-\(n\)-point problem''
Recommended article: Errata to: ``Elimination and fixed point iterations''
Recommended article: Erratum: An algorithm for solving boundary value problems
description: scientific article; zbMATH DE number 3875931