A new Newtons method with diagonal Jacobian approximation for systems of nonlinear equations
Problem statement: The major weaknesses of Newton method for nonlinear equations entail computation of Jacobian matrix and solving systems of n linear equations in each of the iterations. Approach: In some extent function derivatives are quit costly and Jacobian is computationally expensive which r...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Science Publications
2010
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/12751/1/A%20new%20Newtons%20method%20with%20diagonal%20Jacobian%20approximation%20for%20systems%20of%20nonlinear%20equations.pdf |
| _version_ | 1825945104092758016 |
|---|---|
| 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 | Problem statement: The major weaknesses of Newton method for nonlinear equations entail computation of Jacobian matrix and solving systems of n linear equations in each of the iterations. Approach: In some extent function derivatives are quit costly and Jacobian is
computationally expensive which requires evaluation (storage) of n×n matrix in every iteration. Results: This storage requirement became unrealistic when n becomes large. We proposed a new method that approximates Jacobian into diagonal matrix which aims at reducing the storage
requirement, computational cost and CPU time, as well as avoiding solving n linear equations in each iterations.
Conclusion/Recommendations: The proposed method is significantly cheaper than Newton’s method and very much faster than fixed Newton’s method also suitable for small, medium and large scale nonlinear systems with dense or spa
rse Jacobian. Numerical experiments were carried out which shows that, the proposed method is very encouraging. |
| first_indexed | 2024-03-06T07:26:18Z |
| format | Article |
| id | upm.eprints-12751 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:26:18Z |
| publishDate | 2010 |
| publisher | Science Publications |
| record_format | dspace |
| spelling | upm.eprints-127512015-10-30T00:38:46Z http://psasir.upm.edu.my/id/eprint/12751/ A new Newtons method with diagonal Jacobian approximation for systems of nonlinear equations Yusuf, Mohammed Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor Problem statement: The major weaknesses of Newton method for nonlinear equations entail computation of Jacobian matrix and solving systems of n linear equations in each of the iterations. Approach: In some extent function derivatives are quit costly and Jacobian is computationally expensive which requires evaluation (storage) of n×n matrix in every iteration. Results: This storage requirement became unrealistic when n becomes large. We proposed a new method that approximates Jacobian into diagonal matrix which aims at reducing the storage requirement, computational cost and CPU time, as well as avoiding solving n linear equations in each iterations. Conclusion/Recommendations: The proposed method is significantly cheaper than Newton’s method and very much faster than fixed Newton’s method also suitable for small, medium and large scale nonlinear systems with dense or spa rse Jacobian. Numerical experiments were carried out which shows that, the proposed method is very encouraging. Science Publications 2010-09-30 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/12751/1/A%20new%20Newtons%20method%20with%20diagonal%20Jacobian%20approximation%20for%20systems%20of%20nonlinear%20equations.pdf Yusuf, Mohammed Waziri and Leong, Wah June and Abu Hassan, Malik and Monsi, Mansor (2010) A new Newtons method with diagonal Jacobian approximation for systems of nonlinear equations. Journal of Mathematics and Statistics, 6 (3). pp. 246-252. ISSN 1549-3644; ESSN: 1558-6359 10.3844/jmssp.2010.246.252 |
| spellingShingle | Yusuf, Mohammed Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor A new Newtons method with diagonal Jacobian approximation for systems of nonlinear equations |
| title | A new Newtons method with diagonal Jacobian approximation for systems of nonlinear equations |
| title_full | A new Newtons method with diagonal Jacobian approximation for systems of nonlinear equations |
| title_fullStr | A new Newtons method with diagonal Jacobian approximation for systems of nonlinear equations |
| title_full_unstemmed | A new Newtons method with diagonal Jacobian approximation for systems of nonlinear equations |
| title_short | A new Newtons method with diagonal Jacobian approximation for systems of nonlinear equations |
| title_sort | new newtons method with diagonal jacobian approximation for systems of nonlinear equations |
| url | http://psasir.upm.edu.my/id/eprint/12751/1/A%20new%20Newtons%20method%20with%20diagonal%20Jacobian%20approximation%20for%20systems%20of%20nonlinear%20equations.pdf |
| work_keys_str_mv | AT yusufmohammedwaziri anewnewtonsmethodwithdiagonaljacobianapproximationforsystemsofnonlinearequations AT leongwahjune anewnewtonsmethodwithdiagonaljacobianapproximationforsystemsofnonlinearequations AT abuhassanmalik anewnewtonsmethodwithdiagonaljacobianapproximationforsystemsofnonlinearequations AT monsimansor anewnewtonsmethodwithdiagonaljacobianapproximationforsystemsofnonlinearequations AT yusufmohammedwaziri newnewtonsmethodwithdiagonaljacobianapproximationforsystemsofnonlinearequations AT leongwahjune newnewtonsmethodwithdiagonaljacobianapproximationforsystemsofnonlinearequations AT abuhassanmalik newnewtonsmethodwithdiagonaljacobianapproximationforsystemsofnonlinearequations AT monsimansor newnewtonsmethodwithdiagonaljacobianapproximationforsystemsofnonlinearequations |