On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations
The primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub’s conject...
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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/10.1155/2014/272949 |
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| _version_ | 1832568403246710784 |
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| author | Taher Lotfi Alicia Cordero Juan R. Torregrosa Morteza Amir Abadi Maryam Mohammadi Zadeh |
| author_facet | Taher Lotfi Alicia Cordero Juan R. Torregrosa Morteza Amir Abadi Maryam Mohammadi Zadeh |
| author_sort | Taher Lotfi |
| collection | DOAJ |
| description | The primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per
iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub’s conjecture relevant to
construction optimal methods without memory. Moreover, some concrete methods of this class are shown
and implemented numerically, showing their applicability and efficiency. |
| format | Article |
| id | doaj-art-0569ce22241446e7a3572cff95b5724d |
| 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-0569ce22241446e7a3572cff95b5724d2025-02-03T00:59:05ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/272949272949On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear EquationsTaher Lotfi0Alicia Cordero1Juan R. Torregrosa2Morteza Amir Abadi3Maryam Mohammadi Zadeh4Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65188, IranInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, SpainInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, SpainDepartment of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65188, IranDepartment of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65188, IranThe primary goal of this work is to provide a general optimal three-step class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per iteration with eighth-order convergence. Consequently, it satisfies Kung and Traub’s conjecture relevant to construction optimal methods without memory. Moreover, some concrete methods of this class are shown and implemented numerically, showing their applicability and efficiency.http://dx.doi.org/10.1155/2014/272949 |
| spellingShingle | Taher Lotfi Alicia Cordero Juan R. Torregrosa Morteza Amir Abadi Maryam Mohammadi Zadeh On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations The Scientific World Journal |
| title | On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations |
| title_full | On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations |
| title_fullStr | On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations |
| title_full_unstemmed | On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations |
| title_short | On Generalization Based on Bi et al. Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations |
| title_sort | on generalization based on bi et al iterative methods with eighth order convergence for solving nonlinear equations |
| url | http://dx.doi.org/10.1155/2014/272949 |
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