A family of multi-point iterative methods for solving systems of nonlinear equations

We extend to n -dimensional case a known multi-point family of iterative methods for solving nonlinear equations. This family includes as particular cases some well known and also some new methods. The main advantage of these methods is they have order three or four and they do not require the evaluation of any second or higher order Fréchet derivatives. A local convergence analysis and numerical examples are provided.