A reduced composition technique has been used on Newton and Jarratt's methods in order to obtain an optimal relation between convergence order, functional evaluations and number of operations. Following this aim, a family of methods is obtained whose efficiency indices are proved to be better for systems of nonlinear equations.

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ElsevierMartínez Molada, E.; Hueso Pagoaga, JL.; Teruel, C. (2015). Convergence AbstractIn 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.