On the Optimal Choice of Parameters in Two-Point Iterative Methods for Solving Nonlinear Equations

Optimization by parameters in the iterative methods for solving non-linear equations

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In this paper, we used the necessary optimality condition for parameters in a two-point iterations for solving nonlinear equations. Optimal values of these parameters fully coincide with those obtained in [6] and allow us to increase the convergence order of these iterative methods. Numerical experiments and the comparison of existing robust methods are included to confirm the theoretical results and high computational efficiency.

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“…There are some choices of parameters based on the error analysis, see for example [1,2,3,4,5,8,9] and references therein. Recently, researchers have also proposed several biparametric two-step simple methods with and without memory [1, 3,4,6]. On the other hand, optimization by parameters is one of the powerful techniques in science and engineering practice.…”

“…In the last section, we present the results of numerical experiments that confirm the theoretical conclusion about the convergence order and made a comparison with well-known methods of the same order of convergence. In this paper, we consider optimization by parameters in the two-point iterative methods [6,7].…”