A multi-point iterative method for solving nonlinear equations with optimal order of convergence
In this study, a three-point iterative method for solving nonlinear equations is presented. The purpose is to upgrade a fourth order iterative method by adding one Newton step and using a proportional approximation for last derivative. Per iteration this method needs three evaluations of the functi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/72929/ http://psasir.upm.edu.my/id/eprint/72929/1/KUNG.pdf |
| _version_ | 1848857226747314176 |
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| author | Nik Long, Nik Mohd Asri Salimi, Mehdi Sharifi, Somayeh Pansera, Bruno Antonio |
| author_facet | Nik Long, Nik Mohd Asri Salimi, Mehdi Sharifi, Somayeh Pansera, Bruno Antonio |
| author_sort | Nik Long, Nik Mohd Asri |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this study, a three-point iterative method for solving nonlinear equations is presented. The purpose is to upgrade a fourth order iterative method by adding one Newton step and using a proportional approximation for last derivative. Per iteration
this method needs three evaluations of the function and one evaluation of its first derivatives. In addition, the efficiency index of the developed method is √4 8 ≈ 1.682 which supports the Kung-Traub conjecture on the optimal order of convergence. Moreover, numerical and graphical comparison of the proposed method with other existing methods with the same order of convergence are given. |
| first_indexed | 2025-11-15T11:54:11Z |
| format | Article |
| id | upm-72929 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T11:54:11Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-729292020-11-27T20:11:05Z http://psasir.upm.edu.my/id/eprint/72929/ A multi-point iterative method for solving nonlinear equations with optimal order of convergence Nik Long, Nik Mohd Asri Salimi, Mehdi Sharifi, Somayeh Pansera, Bruno Antonio In this study, a three-point iterative method for solving nonlinear equations is presented. The purpose is to upgrade a fourth order iterative method by adding one Newton step and using a proportional approximation for last derivative. Per iteration this method needs three evaluations of the function and one evaluation of its first derivatives. In addition, the efficiency index of the developed method is √4 8 ≈ 1.682 which supports the Kung-Traub conjecture on the optimal order of convergence. Moreover, numerical and graphical comparison of the proposed method with other existing methods with the same order of convergence are given. Springer 2018 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/72929/1/KUNG.pdf Nik Long, Nik Mohd Asri and Salimi, Mehdi and Sharifi, Somayeh and Pansera, Bruno Antonio (2018) A multi-point iterative method for solving nonlinear equations with optimal order of convergence. Japan Journal of Industrial and Applied Mathematics, 35. 497 - 509. ISSN 1868-937X; ESSN: 0916-7005 https://www.researchgate.net/publication/322295964_A_multi-point_iterative_method_for_solving_nonlinear_equations_with_optimal_order_of_convergence/link/5a5bf701aca2727d608a2937/download 10.1007/s13160-017-0294-4 |
| spellingShingle | Nik Long, Nik Mohd Asri Salimi, Mehdi Sharifi, Somayeh Pansera, Bruno Antonio A multi-point iterative method for solving nonlinear equations with optimal order of convergence |
| title | A multi-point iterative method for solving nonlinear equations with optimal order of convergence |
| title_full | A multi-point iterative method for solving nonlinear equations with optimal order of convergence |
| title_fullStr | A multi-point iterative method for solving nonlinear equations with optimal order of convergence |
| title_full_unstemmed | A multi-point iterative method for solving nonlinear equations with optimal order of convergence |
| title_short | A multi-point iterative method for solving nonlinear equations with optimal order of convergence |
| title_sort | multi-point iterative method for solving nonlinear equations with optimal order of convergence |
| url | http://psasir.upm.edu.my/id/eprint/72929/ http://psasir.upm.edu.my/id/eprint/72929/ http://psasir.upm.edu.my/id/eprint/72929/ http://psasir.upm.edu.my/id/eprint/72929/1/KUNG.pdf |