General local convergence theory for a class of iterative processes and its applications to Newton's method
type: Item
instance of: scholarly article
title: General local convergence theory for a class of iterative processes and its applications to Newton's method
zbMATH Open document ID: 1158.65040
author: Petko D. Proinov
published in: Journal of Complexity
publication date: 2009-01-30T00:00:00Z
review text: General local convergence theorems with order of convergence \(r\geq 1\) are provided for iterative processes of type \( x_{n+1}=Tx_{n}\), where \(T:D \subset X \rightarrow X\) is an iteration function in a metric space \(X\). The new local convergence theory is applied to Newton iteration for simple zeros of nonlinear operators in Banach spaces as well as to Schröder iteration for multiple zeros of polynomials and analytic functions.The theory is also applied to establish a general theorem for the uniqueness ball of nonlinear equation in Banach spaces.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 5500793
zbMATH Keywords: iterative methods
zbMATH Keywords: local convergence
zbMATH Keywords: metric spaces
zbMATH Keywords: Newton iteration
zbMATH Keywords: Banach spaces
zbMATH Keywords: Schröder iteration
zbMATH Keywords: polynomial zeros
zbMATH Keywords: zeros of analytical functions
zbMATH Keywords: multiple zeros
MaRDI profile type: Publication
full work available at URL: j.jco.2008.05.006
OpenAlex ID: W1989081312
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DOI: 10.1016/J.JCO.2008.05.006
description: scientific article; zbMATH DE number 5500793