Local analysis of a spectral correction for the Gauss-Newton model applied to quadratic residual problems

Autor(es)

Goncalves, Douglas S. ; Santos, Sandra A.

• Tipo de documento: Artigo Científico
• Fonte: NUMERICAL ALGORITHMS; v. 73, n. 2, p. 407-431, OCT 2016.
• Citações Web of Science: 4

Resumo

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. (AU)

• Processo FAPESP: 13/05475-7 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Linha de fomento: Auxílio à Pesquisa - Temático
• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: José Alberto Cuminato
• Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs