Local convergence analysis of inexact Gauss-Newton like methods under majorant condition

Authors:
O. P. Ferreira;M. L. N. Gonçalves;P. R. Oliveira
Affiliations:
IME/UFG, Campus II- Caixa Postal 131, 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 Computational and Applied Mathematics
Year:
2012

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Abstract

In this paper, we present a local convergence analysis of inexact Gauss-Newton like methods for solving nonlinear least squares problems. Under the hypothesis that the derivative of the function associated with the least squares problem satisfies a majorant condition, we obtain that the method is well-defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the least squares problem. It also allows us to obtain an estimate of convergence ball for inexact Gauss-Newton like methods and some important, special cases.