Local convergence of the Gauss-Newton-Kurchatov method under generalized Lipschitz conditions

Keywords: Gauss-Newton-Kurchatov method, local convergence, Fréchet derivative, divided difference, generalized Lipschitz condition, convergence domain
Published online: 2021-07-28


We investigate the local convergence of the Gauss-Newton-Kurchatov method for solving nonlinear least squares problems. This method is a combination of Gauss-Newton and Kurchatov methods and it is used for problems with the decomposition of the operator. The convergence analysis of the method is performed under the generalized Lipshitz conditions. The conditions of convergence, radius and the convergence order of the considered method are established. Given numerical examples confirm the theoretical results.

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How to Cite
Shakhno S., Yarmola H. Local Convergence of the Gauss-Newton-Kurchatov Method under Generalized Lipschitz Conditions. Carpathian Math. Publ. 2021, 13 (2), 305-314.