Improving the applicability of the secant method to solve nonlinear systems of equations

A modification of the secant method for the approximation of nonlinear system of equations is considered to improve the applicability of the secant method. This modification changes the resolution of a linear system in each step, necessary to apply the secant method, for several matrix multiplications. In this way, the numerical stability of the secant method can be improved. In addition, in this paper, we prove that the modification considered keeps two important properties of the secant method, such as: does not use derivatives in its algorithm and has R-order of convergence at least 1+5/2.