Gauss–Newton–Kurchatov Method for the Solution of Nonlinear Least-Squares Problems

We propose and study an iterative method for the solution of a nonlinear least-squares problem with nondifferentiable operator. In this method, instead of the Jacobian, we use the sum of derivative of the differentiable part of the operator and divided difference with specially chosen points of the nondifferentiable part of operator. We prove a theorem substantiating the process of convergence of the proposed method and establish its rate. We also present the results of numerical experiments carried out for the test problems with nondifferentiable operators.