Abstract and Applied Analysis

Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods

F. Soleymani and S. Shateyi

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Abstract

Optimization problems defined by (objective) functions for which derivatives are unavailable or available at an expensive cost are emerging in computational science. Due to this, the main aim of this paper is to attain as high as possible of local convergence order by using fixed number of (functional) evaluations to find efficient solvers for one-variable nonlinear equations, while the procedure to achieve this goal is totally free from derivative. To this end, we consider the fourth-order uniparametric family of Kung and Traub to suggest and demonstrate two classes of three-step derivative-free methods using only four pieces of information per full iteration to reach the optimal order eight and the optimal efficiency index 1.682. Moreover, a large number of numerical tests are considered to confirm the applicability and efficiency of the produced methods from the new classes.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 318165, 14 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475899

Digital Object Identifier
doi:10.1155/2012/318165

Mathematical Reviews number (MathSciNet)
MR2994915

Zentralblatt MATH identifier
1253.65100

Citation

Soleymani, F.; Shateyi, S. Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods. Abstr. Appl. Anal. 2012 (2012), Article ID 318165, 14 pages. doi:10.1155/2012/318165. https://projecteuclid.org/euclid.aaa/1364475899


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