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

• Autores: José Luis Hueso Pagoaga, Eulalia Martínez Molada, Carles Teruel
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 275, Nº 1, 2015, págs. 412-420
• Idioma: inglés
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• Resumen

  • 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.