  A development of an inverse first-order divided difference operator for
functions of several variables is presented. Two generalized derivative-free
algorithms builded up from Ostrowski's method for solving systems of nonlinear
equations are written and analyzed. A direct computation of the local order of
convergence for these variants of Ostrowski's method is given. In order to
preserve the local order of convergence, any divided difference operator is not
valid. Two counterexamples of computation of a classical divided difference
operator without preserving the order are presented. A new divided difference
operator solving this problem is proposed. Furthermore, a computation that
approximates the order of convergence is generated for the examples and it
confirms in a numerical way that the order of the methods is well deduced.
