On an application of Herzberger’s matrix method to multipoint families of root-solvers

An application of Herzberger?s matrix method, very rarely used in the topic of multipoint methods for solving nonlinear equations, is presented. It is shown that the area of application of Herzberger?s matrix method is wider than it is presented in [J. Herzberger, ?ber Matrixdarstellungen f?r Iterationverfahren bei nichtlinearen Gleichungen, Computing, 12 (1974) 215-222]. This method is applied for the determination of the order of convergence of multipoint families of methods, Steffensen?s type and Newton?s type, with and without memory. The advantage and the elegance of this method arise from ease in handling matrices.