Two-step derivative-free diagonally Newton's method for large-scale nonlinear equations
In this study, we extend the technique of Waziri et al. (2010a) via incorporating the two-step scheme in the framework of the diagonal Jacobian updating method to solve large-scale systems of nonlinear equations. In this approach we used points from two previous steps unlike one step approach in mos...
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| Format: | Article |
| Language: | English |
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IDOSI Publications
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/44356/ http://psasir.upm.edu.my/id/eprint/44356/1/Two-step%20derivative-free%20diagonally%20Newton%27s%20method%20for%20large-scale%20nonlinear%20equations.pdf |
| _version_ | 1848850433287651328 |
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| author | Yusuf, Mohammed Waziri Leong, Wah June Mamat, Mustafa Moyi, Aliyu Usman |
| author_facet | Yusuf, Mohammed Waziri Leong, Wah June Mamat, Mustafa Moyi, Aliyu Usman |
| author_sort | Yusuf, Mohammed Waziri |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this study, we extend the technique of Waziri et al. (2010a) via incorporating the two-step scheme in the framework of the diagonal Jacobian updating method to solve large-scale systems of nonlinear equations. In this approach we used points from two previous steps unlike one step approach in most Newton’s-like methods. The anticipation has been to improve the current Jacobian approximation into a diagonal matrix. Under mild assumptions local convergence of the proposed method is proved. The results of numerical tests are provided to demonstrate the distinctive qualities of this new approach in contrast with other available variants of Newton’s method. The method proposed in this paper has out performs some Newton-like methods in terms of computation cost and storage requirements. |
| first_indexed | 2025-11-15T10:06:13Z |
| format | Article |
| id | upm-44356 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:06:13Z |
| publishDate | 2013 |
| publisher | IDOSI Publications |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-443562020-07-10T01:52:05Z http://psasir.upm.edu.my/id/eprint/44356/ Two-step derivative-free diagonally Newton's method for large-scale nonlinear equations Yusuf, Mohammed Waziri Leong, Wah June Mamat, Mustafa Moyi, Aliyu Usman In this study, we extend the technique of Waziri et al. (2010a) via incorporating the two-step scheme in the framework of the diagonal Jacobian updating method to solve large-scale systems of nonlinear equations. In this approach we used points from two previous steps unlike one step approach in most Newton’s-like methods. The anticipation has been to improve the current Jacobian approximation into a diagonal matrix. Under mild assumptions local convergence of the proposed method is proved. The results of numerical tests are provided to demonstrate the distinctive qualities of this new approach in contrast with other available variants of Newton’s method. The method proposed in this paper has out performs some Newton-like methods in terms of computation cost and storage requirements. IDOSI Publications 2013 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/44356/1/Two-step%20derivative-free%20diagonally%20Newton%27s%20method%20for%20large-scale%20nonlinear%20equations.pdf Yusuf, Mohammed Waziri and Leong, Wah June and Mamat, Mustafa and Moyi, Aliyu Usman (2013) Two-step derivative-free diagonally Newton's method for large-scale nonlinear equations. World Applied Sciences Journal, 21. pp. 86-94. ISSN 1818-4952; ESSN: 1991-6426 https://www.idosi.org/wasj/wasj21(am)2013.htm 10.5829/idosi.wasj.2013.21.am.2045 |
| spellingShingle | Yusuf, Mohammed Waziri Leong, Wah June Mamat, Mustafa Moyi, Aliyu Usman Two-step derivative-free diagonally Newton's method for large-scale nonlinear equations |
| title | Two-step derivative-free diagonally Newton's method for large-scale nonlinear equations |
| title_full | Two-step derivative-free diagonally Newton's method for large-scale nonlinear equations |
| title_fullStr | Two-step derivative-free diagonally Newton's method for large-scale nonlinear equations |
| title_full_unstemmed | Two-step derivative-free diagonally Newton's method for large-scale nonlinear equations |
| title_short | Two-step derivative-free diagonally Newton's method for large-scale nonlinear equations |
| title_sort | two-step derivative-free diagonally newton's method for large-scale nonlinear equations |
| url | http://psasir.upm.edu.my/id/eprint/44356/ http://psasir.upm.edu.my/id/eprint/44356/ http://psasir.upm.edu.my/id/eprint/44356/ http://psasir.upm.edu.my/id/eprint/44356/1/Two-step%20derivative-free%20diagonally%20Newton%27s%20method%20for%20large-scale%20nonlinear%20equations.pdf |