Two-step diagonal Newton method for large-scale systems of nonlinear equations

We propose some improvements on a diagonal Newton´s method for solving large-scale systems of nonlinear equations. In this approach, we use data from two preceding steps to improve the current approximate Jacobian in diagonal form. Via this approach, we can achieve a higher order of accuracy for Jacobian approximation when compares to other existing diagonal-type Newton´s method. The results of our numerical tests, demonstrate a clear enhancement in numerical performance of our proposed method.