Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/327036
Type: Artigo
Title: Local Analysis Of A Spectral Correction For The Gauss-newton Model Applied To Quadratic Residual Problems
Author: Goncalves
Douglas S.; Santos
Sandra A.
Abstract: A simple spectral correction for the Gauss-Newton model applied to nonlinear least squares problems is presented. Such a correction consists in adding a sign-free multiple of the identity to the Hessian of the Gauss-Newton model, being the multiple based on spectral approximations for the Hessians of the residual functions. A detailed local convergence analysis is provided for the resulting method applied to the class of quadratic residual problems. Under mild assumptions, the proposed method is proved to be convergent for problems for which the convergence of the Gauss-Newton method might not be ensured. Moreover, the rate of linear convergence is proved to be better than the Gauss-Newton's one for a class of non-zero residue problems. These theoretical results are illustrated by numerical examples with quadratic and non-quadratic residual problems.
Subject: Nonlinear Least Squares
Quadratic Residues
Spectral Parameter
Gauss-newton Method
Local Convergence
Editor: Springer
Dordrecht
Rights: fechado
Identifier DOI: 10.1007/s11075-016-0101-3
Address: https://link-springer-com.ez88.periodicos.capes.gov.br/article/10.1007%2Fs11075-016-0101-3
Date Issue: 2016
Appears in Collections:Unicamp - Artigos e Outros Documentos

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