An efficient solver for systems of nonlinear equations with singular Jacobian via diagonal updating
It is well known that the quadratic rate of convergence of Newton method for solving nonlinear equations is depends on when the Jacobian is nonsingular in the neighborhood of the solution. Disobeying this condition, i.e. the Jacobian to be singular the convergence is too slow and may even lost. In t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Hikari Ltd.
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/13026/1/An%20efficient%20solver%20for%20systems%20of%20nonlinear%20equations%20with%20singular%20Jacobian%20via%20diagonal%20updating.pdf |
| _version_ | 1796968347690074112 |
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| author | Waziri, Mohammed Yusuf Leong, Wah June Abu Hassan, Malik Monsi, Mansor |
| author_facet | Waziri, Mohammed Yusuf Leong, Wah June Abu Hassan, Malik Monsi, Mansor |
| author_sort | Waziri, Mohammed Yusuf |
| collection | UPM |
| description | It is well known that the quadratic rate of convergence of Newton method for solving nonlinear equations is depends on when the Jacobian is nonsingular in the neighborhood of the solution. Disobeying this condition, i.e. the Jacobian to be singular the convergence is too slow and may even lost. In this paper, we report on design and implementation of an efficient solver for systems of nonlinear equations with singular Jacobian at a solution. Our approach is based on approximation of the Jacobian inverse into a nonsingular diagonal matrix without computing the Jacobian. The proposed algorithm is simple and straightforward to implement. We report on several numerical experiments which shows that, the proposed method is very efficient. |
| first_indexed | 2024-03-06T07:27:07Z |
| format | Article |
| id | upm.eprints-13026 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:27:07Z |
| publishDate | 2010 |
| publisher | Hikari Ltd. |
| record_format | dspace |
| spelling | upm.eprints-130262015-10-20T01:48:22Z http://psasir.upm.edu.my/id/eprint/13026/ An efficient solver for systems of nonlinear equations with singular Jacobian via diagonal updating Waziri, Mohammed Yusuf Leong, Wah June Abu Hassan, Malik Monsi, Mansor It is well known that the quadratic rate of convergence of Newton method for solving nonlinear equations is depends on when the Jacobian is nonsingular in the neighborhood of the solution. Disobeying this condition, i.e. the Jacobian to be singular the convergence is too slow and may even lost. In this paper, we report on design and implementation of an efficient solver for systems of nonlinear equations with singular Jacobian at a solution. Our approach is based on approximation of the Jacobian inverse into a nonsingular diagonal matrix without computing the Jacobian. The proposed algorithm is simple and straightforward to implement. We report on several numerical experiments which shows that, the proposed method is very efficient. Hikari Ltd. 2010 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/13026/1/An%20efficient%20solver%20for%20systems%20of%20nonlinear%20equations%20with%20singular%20Jacobian%20via%20diagonal%20updating.pdf Waziri, Mohammed Yusuf and Leong, Wah June and Abu Hassan, Malik and Monsi, Mansor (2010) An efficient solver for systems of nonlinear equations with singular Jacobian via diagonal updating. Applied Mathematical Sciences, 4 (69-72). pp. 3403-3412. ISSN 1312-885X; ESSN: 1314-7552 http://www.m-hikari.com/ams/ams-2010/ams-69-72-2010/index.html |
| spellingShingle | Waziri, Mohammed Yusuf Leong, Wah June Abu Hassan, Malik Monsi, Mansor An efficient solver for systems of nonlinear equations with singular Jacobian via diagonal updating |
| title | An efficient solver for systems of nonlinear equations with singular Jacobian via diagonal updating |
| title_full | An efficient solver for systems of nonlinear equations with singular Jacobian via diagonal updating |
| title_fullStr | An efficient solver for systems of nonlinear equations with singular Jacobian via diagonal updating |
| title_full_unstemmed | An efficient solver for systems of nonlinear equations with singular Jacobian via diagonal updating |
| title_short | An efficient solver for systems of nonlinear equations with singular Jacobian via diagonal updating |
| title_sort | efficient solver for systems of nonlinear equations with singular jacobian via diagonal updating |
| url | http://psasir.upm.edu.my/id/eprint/13026/1/An%20efficient%20solver%20for%20systems%20of%20nonlinear%20equations%20with%20singular%20Jacobian%20via%20diagonal%20updating.pdf |
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