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The Gauss-Newton's method for solving nonlinear least squares problems isstudied in this paper. Under the hypothesis that the derivative of the functionassociated with the least square problem satisfies a majorant condition, alocal convergence analysis is presented. This analysis allow us to obtain theoptimal convergence radius, the biggest range for the uniqueness of solution,and to unify two previous and unrelated results.

Local convergence analysis of Gauss-Newton's method under majorant condition