Construction of Optimal Derivative-Free Techniques without Memory
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,...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/497023 |
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| author | F. Soleymani D. K. R. Babajee S. Shateyi S. S. Motsa |
| author_facet | F. Soleymani D. K. R. Babajee S. Shateyi S. S. Motsa |
| author_sort | F. Soleymani |
| collection | DOAJ |
| description | 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 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 presented
iterative 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. |
| format | Article |
| id | doaj-art-e91a408ac41a4c36957f93cc81854527 |
| institution | DOAJ |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e91a408ac41a4c36957f93cc818545272025-08-20T03:21:09ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/497023497023Construction of Optimal Derivative-Free Techniques without MemoryF. Soleymani0D. K. R. Babajee1S. Shateyi2S. S. Motsa3Department of Mathematics, Islamic Azad University, Zahedan Branch, Zahedan, IranAllied Network for Policy Research and Advocacy for Sustainability, IEEE, Mauritius, MauritiusDepartment of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South AfricaSchool of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg, South AfricaConstruction 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 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 presented iterative 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.http://dx.doi.org/10.1155/2012/497023 |
| spellingShingle | F. Soleymani D. K. R. Babajee S. Shateyi S. S. Motsa Construction of Optimal Derivative-Free Techniques without Memory Journal of Applied Mathematics |
| title | Construction of Optimal Derivative-Free Techniques without Memory |
| title_full | Construction of Optimal Derivative-Free Techniques without Memory |
| title_fullStr | Construction of Optimal Derivative-Free Techniques without Memory |
| title_full_unstemmed | Construction of Optimal Derivative-Free Techniques without Memory |
| title_short | Construction of Optimal Derivative-Free Techniques without Memory |
| title_sort | construction of optimal derivative free techniques without memory |
| url | http://dx.doi.org/10.1155/2012/497023 |
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