Local convergence analysis of the Gauss-Newton method under a majorant condition

Authors:
O. P. Ferreira;M. L. N. Gonçalves;P. R. Oliveira
Affiliations:
IME/UFG, Campus II- Caixa Postal 131, CEP 74001-970 - Goiínia, GO, Brazil;COPPE-Sistemas, Universidade Federal do Rio de Janeiro, 21945-970 Rio de Janeiro, RJ, Brazil;COPPE-Sistemas, Universidade Federal do Rio de Janeiro, 21945-970 Rio de Janeiro, RJ, Brazil
Venue:
Journal of Complexity
Year:
2011

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Abstract

The Gauss-Newton method for solving nonlinear least squares problems is studied in this paper. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, a local convergence analysis is presented. This analysis allows us to obtain the optimal convergence radius and the biggest range for the uniqueness of stationary point, and to unify two previous and unrelated results.