Unified semi-local convergence for \(k\)-step iterative methods with flexible and frozen linear operator
type: Item
instance of: scholarly article
title: Unified semi-local convergence for \(k\)-step iterative methods with flexible and frozen linear operator
zbMATH Open document ID: 1468.65050
author: Ioannis Konstantinos Argyros
author: Santhosh George
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: Summary: The aim of this article is to present a unified semi-local convergence analysis for a \(k\)-step iterative method containing the inverse of a flexible and frozen linear operator for Banach space valued operators. Special choices of the linear operator reduce the method to the Newton-type, Newton's, or Stirling's, or Steffensen's, or other methods. The analysis is based on center, as well as Lipschitz conditions and our idea of the restricted convergence region. This idea defines an at least as small region containing the iterates as before and consequently also a tighter convergence analysis.
Mathematics Subject Classification ID: 65J10
zbMATH DE Number: 6994836
zbMATH Keywords: Banach space
zbMATH Keywords: \(k\)-step method
zbMATH Keywords: semi-local convergence
zbMATH Keywords: Lipschitz conditions
MaRDI profile type: Publication
full work available at URL: math6110233
OpenAlex ID: W2898834108
cites work: On two families of high order Newton type methods
cites work: On two high‐order families of frozen Newton‐type methods
cites work: On the semilocal convergence of efficient Chebyshev-secant-type methods
cites work: Weaker conditions for the convergence of Newton's method
cites work: Q4595134
cites work: Iterative Methods and Their Dynamics with Applications
cites work: An eighth-order family of optimal multiple root finders and its dynamics
cites work: Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation
cites work: Q3943431
cites work: Semilocal convergence of a k-step iterative process and its application for solving a special kind of conservative problems
cites work: An efficient fourth order weighted-Newton method for systems of nonlinear equations
Wikidata QID: Q129001090
DOI: 10.3390/MATH6110233
description: scientific article; zbMATH DE number 6994836