Convergence of the Gauss–Newton method for a special class of systems of equations under a majorant condition

Abstract

In this paper, we study the Gauss–Newton method for a special class of systems of non-linear equation. On the hypothesis that the derivative of the function under consideration satisfies a majorant condition, semi-local convergence analysis is presented. In this analysis, the conditions and proof of convergence are simplified by using a simple majorant condition to define regions where the Gauss–Newton sequence is ‘well behaved’. Moreover, special cases of the general theory are presented as applications.

Keywords:

• Gauss–Newton method
• majorant condition
• non-linear systems of equations
• semi-local convergence

Acknowledgments

M.L.N. Gonçalves was supported in part by CAPES-Brazil. P.R. Oliveira author was supported in part by CNPq.