Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior

Authors:
A. Cordero;M. Fardi;M. Ghasemi;J. R. Torregrosa
Affiliations:
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain;Department of Mathematics, Islamic Azad University, Najafabad Branch, Najafabad, Iran;Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, Iran;Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain
Venue:
Calcolo: a quarterly on numerical analysis and theory of computation
Year:
2014

Citing 4
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Abstract

In this paper, we present a family of optimal, in the sense of Kung---Traub's conjecture, iterative methods for solving nonlinear equations with eighth-order convergence. Our methods are based on Chun's fourth-order method. We use the Ostrowski's efficiency index and several numerical tests in order to compare the new methods with other known eighth-order ones. We also extend this comparison to the dynamical study of the different methods.