On a New Three-Step Class of Methods and Its Acceleration for Nonlinear Equations
A class of derivative-free methods without memory for approximating a simple zero of a nonlinear equation is presented. The proposed class uses four function evaluations per iteration with convergence order eight. Therefore, it is an optimal three-step scheme without memory based on Kung-Traub conje...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/134673 |
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| _version_ | 1832551529538650112 |
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| author | T. Lotfi K. Mahdiani Z. Noori F. Khaksar Haghani S. Shateyi |
| author_facet | T. Lotfi K. Mahdiani Z. Noori F. Khaksar Haghani S. Shateyi |
| author_sort | T. Lotfi |
| collection | DOAJ |
| description | A class of derivative-free methods without memory for approximating a simple zero of a nonlinear equation is presented. The proposed class uses four function evaluations per iteration with convergence order eight. Therefore, it is an optimal three-step scheme without memory based on Kung-Traub conjecture. Moreover, the proposed class has an accelerator parameter with the property that it can increase the convergence rate from eight to twelve without any new functional evaluations. Thus, we construct a with memory method that increases considerably efficiency index from 81/4≈1.681 to 121/4≈1.861. Illustrations are also included to support the underlying theory. |
| format | Article |
| id | doaj-art-4462881b98fc4720ab01bf2fa3677b0f |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-4462881b98fc4720ab01bf2fa3677b0f2025-02-03T06:01:09ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/134673134673On a New Three-Step Class of Methods and Its Acceleration for Nonlinear EquationsT. Lotfi0K. Mahdiani1Z. Noori2F. Khaksar Haghani3S. Shateyi4Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, IranDepartment of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, IranDepartment of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, IranDepartment of Mathematics, Islamic Azad University, Shahrekord Branch, Shahrekord, IranDepartment of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, Thohoyandou 0950, South AfricaA class of derivative-free methods without memory for approximating a simple zero of a nonlinear equation is presented. The proposed class uses four function evaluations per iteration with convergence order eight. Therefore, it is an optimal three-step scheme without memory based on Kung-Traub conjecture. Moreover, the proposed class has an accelerator parameter with the property that it can increase the convergence rate from eight to twelve without any new functional evaluations. Thus, we construct a with memory method that increases considerably efficiency index from 81/4≈1.681 to 121/4≈1.861. Illustrations are also included to support the underlying theory.http://dx.doi.org/10.1155/2014/134673 |
| spellingShingle | T. Lotfi K. Mahdiani Z. Noori F. Khaksar Haghani S. Shateyi On a New Three-Step Class of Methods and Its Acceleration for Nonlinear Equations The Scientific World Journal |
| title | On a New Three-Step Class of Methods and Its Acceleration for Nonlinear Equations |
| title_full | On a New Three-Step Class of Methods and Its Acceleration for Nonlinear Equations |
| title_fullStr | On a New Three-Step Class of Methods and Its Acceleration for Nonlinear Equations |
| title_full_unstemmed | On a New Three-Step Class of Methods and Its Acceleration for Nonlinear Equations |
| title_short | On a New Three-Step Class of Methods and Its Acceleration for Nonlinear Equations |
| title_sort | on a new three step class of methods and its acceleration for nonlinear equations |
| url | http://dx.doi.org/10.1155/2014/134673 |
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