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.