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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Ferreira, O. P.²  Goncalves, M. L. N.¹  Oliveira, P. R.¹ 

[1] Univ Fed Rio de Janeiro, COPPE Sistemas, BR-21945970 Rio De Janeiro, RJ, Brazil

[2] IME UFG, BR-74001970 Goiania, Go, Brazil

关键词: Nonlinear least squares problems;    Inexact Gauss-Newton like methods;    Majorant condition;    Local convergence;   

DOI  :  10.1016/j.cam.2011.12.008

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free