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Abstract

There are a lot of dierent physical processes modeling of which lead us to a nonlinear least squares problems. Usually, they arise in cases of modeling or evaluating physical processes by values obtained as a result of measurements. In this article, we consider problems in which the nonlinear function consists of a dierentiable and nondierentiable part. For numerical solving such nonlinear least-squares problems, we proposed the Gauss-NewtonPotra method. Since the full Jacobian does not exist, this method uses instead of Jacobian the sum of the derivative of the dierentiable part of the operator and the combination of rst-order divided dierences of the nondierentiable part of the operator. The local convergence analysis of the method is conducted under the generalized Lipschitz conditions for rst-order derivatives and rst- and second-order divided dierences. These conditions, instead of Lipschitz constant, contain some positive integrable function. The classical Lipschitz conditions are a partial case of the generalized Lipschitz conditions. An equation for the radius of convergence domain and error estimates were obtained. A convergence order of the method in case of zero residual was established. We carry out numerical experiments on a set of test problems and compare results with other known methods by the number of iterations. The obtained results show that the Gauss-Newton-Potra method is more ecient than iterative-dierence methods.