Newton method for nonlinear system with singular Jacobian using diagonal updating
It is well known that when the Jacobian of nonlinear systems is nonsingular in the neighborhood of the solution, the convergence of Newton method to a solution x* of F(x) = 0 is guaranteed and the rate is quadratic. Violating this condition, i.e. the Jacobian to be singular the convergence may be un...
Main Authors: | , , , |
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Format: | Article |
Language: | English |
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Centre for Environment, Social and Economic Research Publications
2010
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Online Access: | http://psasir.upm.edu.my/id/eprint/15810/1/Newton%20method%20for%20nonlinear%20system%20with%20singular%20Jacobian%20using%20diagonal%20updating.pdf |
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author | Yusuf, Mohammed Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor |
author_facet | Yusuf, Mohammed Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor |
author_sort | Yusuf, Mohammed Waziri |
collection | UPM |
description | It is well known that when the Jacobian of nonlinear systems is nonsingular in the neighborhood of the solution, the convergence of Newton method to a solution x* of F(x) = 0 is guaranteed and the rate is quadratic. Violating this condition, i.e. the Jacobian to be singular the convergence may be unsatisfactory and may even lost. In this paper we present a modification of Newton method for systems of nonlinear equations with singular Jacobian which is very much faster and significantly cheaper than both Newton and Fixed Newton methods. This is made possible by approximating the Jacobian into a nonsingular diagonal matrix. Numerical experiments are carried out which shows that, the proposed method is very encouraging. |
first_indexed | 2024-03-06T07:35:27Z |
format | Article |
id | upm.eprints-15810 |
institution | Universiti Putra Malaysia |
language | English |
last_indexed | 2024-03-06T07:35:27Z |
publishDate | 2010 |
publisher | Centre for Environment, Social and Economic Research Publications |
record_format | dspace |
spelling | upm.eprints-158102015-10-30T00:41:29Z http://psasir.upm.edu.my/id/eprint/15810/ Newton method for nonlinear system with singular Jacobian using diagonal updating Yusuf, Mohammed Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor It is well known that when the Jacobian of nonlinear systems is nonsingular in the neighborhood of the solution, the convergence of Newton method to a solution x* of F(x) = 0 is guaranteed and the rate is quadratic. Violating this condition, i.e. the Jacobian to be singular the convergence may be unsatisfactory and may even lost. In this paper we present a modification of Newton method for systems of nonlinear equations with singular Jacobian which is very much faster and significantly cheaper than both Newton and Fixed Newton methods. This is made possible by approximating the Jacobian into a nonsingular diagonal matrix. Numerical experiments are carried out which shows that, the proposed method is very encouraging. Centre for Environment, Social and Economic Research Publications 2010-09 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/15810/1/Newton%20method%20for%20nonlinear%20system%20with%20singular%20Jacobian%20using%20diagonal%20updating.pdf Yusuf, Mohammed Waziri and Leong, Wah June and Abu Hassan, Malik and Monsi, Mansor (2010) Newton method for nonlinear system with singular Jacobian using diagonal updating. International Journal of Mathematics and Computations, 8 (S10). pp. 1-8. ISSN 0974-5718; ESSN: 0974-570X |
spellingShingle | Yusuf, Mohammed Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor Newton method for nonlinear system with singular Jacobian using diagonal updating |
title | Newton method for nonlinear system with singular Jacobian using diagonal updating |
title_full | Newton method for nonlinear system with singular Jacobian using diagonal updating |
title_fullStr | Newton method for nonlinear system with singular Jacobian using diagonal updating |
title_full_unstemmed | Newton method for nonlinear system with singular Jacobian using diagonal updating |
title_short | Newton method for nonlinear system with singular Jacobian using diagonal updating |
title_sort | newton method for nonlinear system with singular jacobian using diagonal updating |
url | http://psasir.upm.edu.my/id/eprint/15810/1/Newton%20method%20for%20nonlinear%20system%20with%20singular%20Jacobian%20using%20diagonal%20updating.pdf |
work_keys_str_mv | AT yusufmohammedwaziri newtonmethodfornonlinearsystemwithsingularjacobianusingdiagonalupdating AT leongwahjune newtonmethodfornonlinearsystemwithsingularjacobianusingdiagonalupdating AT abuhassanmalik newtonmethodfornonlinearsystemwithsingularjacobianusingdiagonalupdating AT monsimansor newtonmethodfornonlinearsystemwithsingularjacobianusingdiagonalupdating |