Convergence of the Gauss-Newton method for a special class of systems of   equations under a majorant condition
  In this paper, we study the Gauss-Newton method for a special class of systems of nonlinear equation. Under 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. 
Max L. N. Gon\c{c}alves and Paulo R. Oliveira
math.OC