Convergence analysis of the GaussNewton Potra method for nonlinear least squares problems 

Author 
stepan.shakhno@lnu.edu.ua^{1}, halyna.yarmola@lnu.edu.ua^{2}, yuriy.shunkin@lnu.edu.ua^{3}
Faculty of Applied Mathematics and Informatics,
Ivan Franko National University of Lviv, Lviv, Ukraine

Abstract 
In this paper we study an iterative differentialdifference 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 firstorder 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.

Keywords 
least squares problem; decomposition of operator; GaussNewtonPotra method; omegaconditions;
divided differences

DOI 
doi:10.15330/ms.50.2.211221

Reference 
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Pages 
211221

Volume 
50

Issue 
2

Year 
2018

Journal 
Matematychni Studii

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