Construction of Optimal Derivative-Free Techniques without Memory
Joint Authors
Soleymani, Fazlollah
Babajee, D. K. R.
Shateyi, Stanford
Motsa, Sandile Sydney
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-11-20
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
Construction of iterative processes without memory, which are both optimal according to the Kung-Traub hypothesis and derivative-free, is considered in this paper.
For this reason, techniques with four and five function evaluations per iteration, which reach to the optimal orders eight and sixteen, respectively, are discussed theoretically.
These schemes can be viewed as the generalizations of the recent optimal derivative-free family of Zheng et al.
in (2011).
This procedure also provides an n-step family using n+1 function evaluations per full cycle to possess the optimal order 2n.
The analytical proofs of the main contributions are given and numerical examples are included to confirm the outstanding convergence speed of the presentediterative methods using only few function evaluations.
The second aim of this work will be furnished when a hybrid algorithm for capturing all the zeros in an interval has been proposed.
The novel algorithm could deal with nonlinear functions having finitely many zeros in an interval.
American Psychological Association (APA)
Soleymani, Fazlollah& Babajee, D. K. R.& Shateyi, Stanford& Motsa, Sandile Sydney. 2012. Construction of Optimal Derivative-Free Techniques without Memory. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-24.
https://search.emarefa.net/detail/BIM-1028908
Modern Language Association (MLA)
Soleymani, Fazlollah…[et al.]. Construction of Optimal Derivative-Free Techniques without Memory. Journal of Applied Mathematics No. 2012 (2012), pp.1-24.
https://search.emarefa.net/detail/BIM-1028908
American Medical Association (AMA)
Soleymani, Fazlollah& Babajee, D. K. R.& Shateyi, Stanford& Motsa, Sandile Sydney. Construction of Optimal Derivative-Free Techniques without Memory. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-24.
https://search.emarefa.net/detail/BIM-1028908
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1028908