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

F. Soleymani and S. Shateyi

Abstract and Applied Analysis, 2012, vol. 2012, 1-14

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.

Date: 2012
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2012/318165.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2012/318165.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:318165

DOI: 10.1155/2012/318165

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().