Convergence and uniqueness properties of Gauss-Newtonʹs method

The generalized radius and center Lipschitz conditions with L average are introduced to investigate the convergence of Gauss-Newtonʹs method for finding the nonlinear least squares solution of nonlinear equations. The radii of the convergence ball of Gauss-Newtonʹs method and the uniqueness ball of the solution are estimated. Some applications are given.