New efficient multipoint iterative methods for solving nonlinear systems

It is attempted to put forward a new multipoint iterative method for approximating solutions of nonlinear systems. The main feature of the extended methods is that it uses only one LU factorization which preserves and reduces computational complexities. Moreover, the first step is designed in such a way that in most cases singularity of the denominator is avoided. Therefore, we try to generalize the suggested method so that we can increase the order of convergence from four to six and eight, but we do not need any new LU factorization. Also, we justify this advantage of the convergence analysis versus some numerical methods with different examples.