Convergence of Gauss-Newton's method and uniqueness of the solution

In this paper, we study the convergence of Gauss-Newton's method for nonlinear least squares problems. Under the hypothesis that derivative satisfies some kinds of weak Lipschitz condition, we obtain the exact estimates of the radii of convergence ball of Gauss-Newton's method and the uniqueness ball of the solution. New results can be used to determinate approximation zero of Gauss-Newton's method.