Convergence results for a fast iterative method in linear spaces
type: Item
instance of: scholarly article
title: Convergence results for a fast iterative method in linear spaces
zbMATH Open document ID: 0939.65089
author: Ioannis Konstantinos Argyros
published in: Taiwanese Journal of Mathematics
publication date: 2000-07-10T00:00:00Z
review text: Recently, the author proposed a fast iterative method for solving the nonlinear equation \(F(x)= 0\), where \(F\) is a twice Fréchet differentiable operator defined on some convex subset \(D\) of a Banach space \(E_1\) with values in a Banach space \(E_2\). Using standard Newton-Kantorovich assumption he proved that under Lipschitz-type hypotheses on an upper bound of the same derivative the iterative method under review has the order of convergence equal to four. In this paper, he relaxed these conditions using Lipschitz-hypotheses on the first Fréchet-derivative only and examines the monotone convergence of the same method in a partially ordered topological space setting.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H07
zbMATH DE Number: 1370638
zbMATH Keywords: Fréchet-derivative majorant method
zbMATH Keywords: fast iterative method
zbMATH Keywords: Banach space
zbMATH Keywords: monotone convergence
zbMATH Keywords: partially ordered topological space
reviewed by: Otu Vaarmann
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500407132
OpenAlex ID: W4246664855
DOI: 10.11650/TWJM/1500407132
Recommended article: Q3470048
Recommended article: Convergence of nested classical iterative methods for linear systems
Recommended article: On accelerating the convergence of nonlinear iterative algorithms
Recommended article: Q3077275
Recommended article: Q3221292
Recommended article: Accelerating the convergence speed of iterative methods for solving nonlinear systems
Recommended article: Q5751852
Recommended article: Q5618887
Recommended article: Q4669761
Recommended article: Q5484318
description: scientific article; zbMATH DE number 1370638