On the superlinear convergence of the successive approximations method
type: Item
instance of: scholarly article
title: On the superlinear convergence of the successive approximations method
zbMATH Open document ID: 1012.65042
DOI: 10.1023/A:1015304720071
published in: Journal of Optimization Theory and Applications
publication date: 2002-10-08T00:00:00Z
review text: Successive approximation \(x_{k+1}= G(x_k)\) is considered and its high convergence order in terms of some spectral elements of \(G'(x^*)\) is examined. The author shows that the set of trajectories with high convergence orders is restricted to some affine subspaces, regardless of the nonlinearity of \(G\). The stability of the successive approximations under perturbations is also analyzed.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 1812456
zbMATH Keywords: superlinear convergence
zbMATH Keywords: successive approximations
zbMATH Keywords: convergence orders
zbMATH Keywords: inexact Newton method
zbMATH Keywords: stability
author: Emil Cătinaş
reviewed by: F. Szidarovszky
describes a project that uses: KELLEY
MaRDI profile type: Publication
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full work available at URL: a:1015304720071
OpenAlex ID: W2096245308
description: scientific article; zbMATH DE number 1812456