Hybridization of multi-step iterative process with double direction method for solving a system of nonlinear equations and application to motion control

Abstract This article presents a multi-step algorithm for solving a system of nonlinear equations using a double direction approach with application to motion control. In order to offer a useful derivative-free technique, the acceleration parameter is calculated to rougthly approximate the Jacobian matrix. With the aid of an inexact line search approach, the step-length was calculated. In addition, the proposed method is proving to be globally convergent under some appropriate conditions. Numerical experiment for some large-scale benchmark test problems reported in 1 this article shows the efficiency of the suggested methods compared with the current methods in the literature.