Lipschitz condition

We present a local convergence analysis of the Gauss-Newton-Kurchatov method  for solving nonlinear least squares problems with the decomposition of the operator.  The method uses the sum of the derivative of the differentiable part of the operator and the divided difference of the nondifferentiable part instead of computing  the full Jacobian.  A theorem, which establishes the conditions of convergence, radius, and the convergence order of the proposed method, is proved [1].  However, the radius of convergence is small in general limiting the choice of initial points.  Using tighter estima