An Improved Derivative-Free Method Via Double Direction Approach for Solving Systems of Nonlinear Equations

We present some double direction method for solving large-scale system of nonlinear equations. This method used the special form of iteration by introducing the two direction vectors in different ways. The approximation to the Jacobian matrix is done by sufficiently constructed diagonal matrix via acceleration parameter as well as derivative-free line search procedure. The proposed method is proved to be globally convergent under mild condition. Finally, numerical comparison using a large scale benchmark test problems show that the proposed method is very promising.