Analysing the efficiency of some modifications of the secant method

Some modifications of the secant method for solving nonlinear equations are revisited and the local order of convergence is found in a direct symbolic computation. To do this, a development of the inverse of the first order divided differences of a function of several variables in two points is presented. A generalisation of the efficiency index used in the scalar case to several variables is also analysed in order to use the most competitive algorithm.