A note on solving nonlinear equations and the natural criterion function
type: Item
instance of: scholarly article
title: A note on solving nonlinear equations and the natural criterion function
zbMATH Open document ID: 0622.90074
DOI: 10.1007/BF00939050
published in: Journal of Optimization Theory and Applications
publication date: 1987-01-01T00:00:00Z
review text: We consider the natural criterion function for controlling a damped Newton iteration used for solving systems of nonlinear equations. An example is given which shows that the method can cycle in an undesirable manner, not possible when using the more conventional test-squares criterion function. Despite this, the natural criterion function is of value in particular applications. This point is illustrated using a system derived from a nonlinear two-point boundary-value problem.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 49M37
zbMATH DE Number: 4010227
zbMATH Keywords: affine invariance
zbMATH Keywords: cycling
zbMATH Keywords: initial scaling
zbMATH Keywords: damped Newton iteration
zbMATH Keywords: systems of nonlinear equations
zbMATH Keywords: nonlinear two-point boundary-value
author: Uri M. Ascher
author: Michael R. Osborne
describes a project that uses: COLSYS
MaRDI profile type: Publication
cites work: Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
cites work: Q3882253
cites work: A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting
cites work: Collocation Software for Boundary-Value ODEs
full work available at URL: https://doi.org/10.1007/bf00939050
OpenAlex ID: W2000970928
description: scientific article; zbMATH DE number 4010227