Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior (Q2017952)

A family of optimal, in the sense of \textit{H. T. Kung} and \textit{J. F. Traub}'s conjecture [J. Assoc. Comput. Mach. 21, 643--651 (1974; Zbl 0289.65023)], iterative methods for solving nonlinear equations with eighth-order of convergence is obtained. The methods are based on \textit{C. Chun}'s fourth-order method [Appl. Math. Comput. 190, No. 1, 57--62 (2007; Zbl 1122.65328)]. \textit{A. M. Ostrowski}'s effciency index [Solutions of equations and systems of equations. Academic Press, New York (1966)] and several numerical tests in order to compare the new methods with other known eighth-order ones are used.