On Geometric Constructions of third order methods for multiple roots of nonlinear equations

The object of the present work is to give geometric constructions of third order methods obtained from the Traub-Gander class for multiple roots when the multiplicity is known. Also, new families of methods for solving nonlinear equations of third order with multiple roots and their geometric construction are presented. Finally, several numerical examples to show the performance of some members of the families mentioned are presented