Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear system

[EN] In this work we present a new family of iterative methods for solving nonlinear systems that are optimal in the sense of Kung and Traub’s conjecture for the unidimensional case. We generalize this family by performing a new step in the iterative method, getting a new family with order of convergence six. We study the efficiency of these families for the multidimensional case by introducing a new term in the computational cost defined by Grau-Sánchez et al. A comparison with already known methods is done by studying the dynamics of these methods in an example system.This research has been supported by Ministerio de Ciencia e Innovacion MTM2011-28636-C02-02 and by Vicerrectorado de Investigacion Universitat Politecnica de Valencia PAID-SP-2012-0498 and PAID-SP-2012-0474.Hueso Pagoaga, JL.; Martínez Molada, E.; Teruel, C. (2015). Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear system. Journal of Computational and Applied Mathematics. 275:420-412. https://doi.org/10.1016/j.cam.2014.06.01042041227