Abstract
In this paper, we present two new iterative methods for solving nonlinear equations by using suitable Taylor and divided difference approximations. Both methods are obtained by modifying PotraPták-s method trying to get optimal order. We prove that the new methods reach orders of convergence four and eight with three and four functional evaluations, respectively. So, Kung and Traub-s conjecture Kung and Traub (1974) [2], that establishes for an iterative method based on n evaluations an optimal order p D 2n1 is fulfilled, getting the highest efficiency indices for orders p D 4 and p D 8, which are 1.587 and 1.682. We also perform different numerical tests that confirm the theoretical results and allow us to compare these methods with Potra-Pták-s method from which they have been derived, and with other recently published eighth-order methods. 2010 Elsevier B.V. All rights reserved.
Keywords
Divided differences Linear interpolation Nonlinear equations Iterative methods Convergence order Efficiency index
Referencia
A. Cordero, J.L. Hueso, E. MartÃÂnez, J.R. Torregrosa. New modifications of PotraPták-s method with optimal fourth and eighth orders of convergence. Journal of Computational and Applied Mathematics 234 (2010) 2969-2976.
