Gauss--Newton--Kurchatov method for the solution of non-linear least-square problems using ω-condition

Abstract

Abstract We propose to study the convergence of an iterative method used for solving non-linear least-square problems having differentiable as well as non-differentiable functions. We use the ω-condition on both first order divided difference of non-differentiable part and first order derivative of differentiable part to establish the condition for convergence of the method. We also present some numerical experiments as test beds for the proposed method. In all the numerical examples, we have compared our results with a well-known Gauss–Newton–Potra method and shown that our convergence analysis gives better error bounds.