Solving systems of nonlinear equations using improved double direction method

The fundamental reason behind double direction approach is that, there are two corrections in the scheme. If one correction fails during iterative process then the other one will correct the system. Therefore, this research aims to present a derivative-free method for solving large-scale system of nonlinear equations via double direction approach. The acceleration parameter used in this approach approximated the Jacobian matrix in order to form a derivative-free method by reducing two direction presented in double direction scheme into a single one. under mild conditions, the proposed method is proved to be globally convergent using derivative-free line search. Numerical results recorded in this paper using a set of large-scale test problems show that the proposed approach is successful for solving large-scale problems.