On an iterative algorithm of order 1.839… for solving the nonlinear least squares problems

In the present paper for solving the nonlinear least-squares problem we propose new free-derivative iteration method with the order of convergence 1.839… We have elaborated the scheme of proof, by which from one point of view the theoretical research of one class of difference iterative methods with different orders of convergence have been conducted. By the results of numerical experiment, the new method is compared with the known difference methods and with the classic Gauss-Newton method.