A New Optimal Eighth-Order Ostrowski-Type Family of Iterative Methods for Solving Nonlinear Equations. (13th March 2014)

• Record Type: Journal Article
• Authors: Lotfi, Taher; Eftekhari, Tahereh
• Other Names: Guo Q. Academic Editor.; Li Z.-Y. Academic Editor.
• Is Part Of: Chinese journal of mathematics. Volume 2014(2014)
• Publication Date: 2014-03-13
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals
• DOI: 10.1155/2014/369713
• Languages: English
• ISSNs: 2314-8071

Abstract

Abstract : Based on Ostrowski's method, a new family of eighth-order iterative methods for solving nonlinear equations by using weight function methods is presented. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative. Therefore, this family of methods has the efficiency index which equals 1.682. Kung and Traub conjectured that a multipoint iteration without memory based onn evaluations could achieve optimal convergence order2 n − 1 . Thus, we provide a new class which agrees with the conjecture of Kung-Traub forn = 4 . Numerical comparisons are made to show the performance of the presented methods.