Convergence analysis of the Gauss-Newton- Potra method for nonlinear least squares problems

S. M. Shakhno1, H. P. Yarmola2, Yu. V. Shunkin2
Faculty of Applied Mathematics and Informatics, Ivan Franko National University of Lviv, Lviv, Ukraine
In this paper we study an iterative differential-difference method for solving nonlinear least squares problems with nondifferentiable residual function. We have proved theorems which establish the conditions of convergence, radius and the convergence order under Lipschitz and $\omega$-conditions for the first-order derivatives of the differentiable part and for the first and second orders divided differences of the nondifferentiable part of the nonlinear function. The carried numerical experiments demonstrate the efficiency of the proposed method.
least squares problem; decomposition of operator; Gauss-Newton-Potra method; omega-conditions; divided differences
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