Artículos de revistas
Local Analysis Of A Spectral Correction For The Gauss-newton Model Applied To Quadratic Residual Problems
Registro en:
Numerical Algorithms. Springer, v. 73, p. 407 - 431, 2016.
1017-1398
1572-9265
WOS:000384427100006
10.1007/s11075-016-0101-3
Autor
Goncalves
Douglas S.; Santos
Sandra A.
Institución
Resumen
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) 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. 73 2 407 431 CNPq [304032/2010-7] FAPESP [2013/05475-7, 2013/07375-0] PRONEX-Optimization Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)