A multidimensional generalization of some classes of iterative methods

In this paper we extend to the multidimensional case some iterative methods that are known in their scalar version. All the schemes considered here are two-step methods with fourth-order local convergence, where the first step is Newton’s method. We analyze the efficiency of these new four algorithms and compare them in terms of the elapsed time needed for their computational implementation. We illustrate our results with some numerical examples and an application to the resolution of the systems arising from a Hammerstein’s integral equation.