Third Order Root-Finding Methods based on a Generalization of Gander's Result

In this paper, a generalization of a classical result by Gander concerning the characterization of third-order methods is addressed. New and classical methods are included in the family. In particular, a new construction of the well-known Chebyshev method is presented. Other methods, based on exponential and logarithmic fittings respectively, are rediscovered too. The proposed methods have a local cubic order of convergence and can be competitive with other third-order methods in the literature, as can be seen from the numerical examples presented.