Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices
Two families of derivative-free methods without memory for approximating a simple zero of a nonlinear equation are presented. The proposed schemes have an accelerator parameter with the property that it can increase the convergence rate without any new functional evaluations. In this way, we constru...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/912796 |
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| _version_ | 1832548077203881984 |
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| author | T. Lotfi F. Soleymani Z. Noori A. Kılıçman F. Khaksar Haghani |
| author_facet | T. Lotfi F. Soleymani Z. Noori A. Kılıçman F. Khaksar Haghani |
| author_sort | T. Lotfi |
| collection | DOAJ |
| description | Two families of derivative-free methods without memory for approximating a simple zero of a nonlinear equation are presented. The proposed schemes have an accelerator parameter with the property that it can increase the convergence rate without any new functional evaluations. In this way, we construct a method with memory that increases considerably efficiency index from 81/4≈1.681 to 121/4≈1.861. Numerical examples and comparison with the existing methods are included to confirm theoretical results and high computational efficiency. |
| format | Article |
| id | doaj-art-aeb882cb37a14fcf9908ede14858441d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-aeb882cb37a14fcf9908ede14858441d2025-02-03T06:42:21ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/912796912796Efficient Iterative Methods with and without Memory Possessing High Efficiency IndicesT. Lotfi0F. Soleymani1Z. Noori2A. Kılıçman3F. Khaksar Haghani4Department of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, IranDepartment of Mathematics, Islamic Azad University, Shahrekord Branch, Shahrekord, IranDepartment of Mathematics, Islamic Azad University, Hamedan Branch, Hamedan, IranDepartment of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, MalaysiaDepartment of Mathematics, Islamic Azad University, Shahrekord Branch, Shahrekord, IranTwo families of derivative-free methods without memory for approximating a simple zero of a nonlinear equation are presented. The proposed schemes have an accelerator parameter with the property that it can increase the convergence rate without any new functional evaluations. In this way, we construct a method with memory that increases considerably efficiency index from 81/4≈1.681 to 121/4≈1.861. Numerical examples and comparison with the existing methods are included to confirm theoretical results and high computational efficiency.http://dx.doi.org/10.1155/2014/912796 |
| spellingShingle | T. Lotfi F. Soleymani Z. Noori A. Kılıçman F. Khaksar Haghani Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices Discrete Dynamics in Nature and Society |
| title | Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices |
| title_full | Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices |
| title_fullStr | Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices |
| title_full_unstemmed | Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices |
| title_short | Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices |
| title_sort | efficient iterative methods with and without memory possessing high efficiency indices |
| url | http://dx.doi.org/10.1155/2014/912796 |
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