Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods
Joint Authors
Soleymani, Fazlollah
Shateyi, Stanford
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-01
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Soleymani, Fazlollah& Shateyi, Stanford. 2012. Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-463076
Modern Language Association (MLA)
Soleymani, Fazlollah& Shateyi, Stanford. Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods. Abstract and Applied Analysis No. 2012 (2012), pp.1-14.
https://search.emarefa.net/detail/BIM-463076
American Medical Association (AMA)
Soleymani, Fazlollah& Shateyi, Stanford. Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-14.
https://search.emarefa.net/detail/BIM-463076
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-463076