Jacobian computation-free Newton's method for systems of nonlinear equations.
We propose a modification to Newton’s method for solving nonlinear equations,namely a Jacobian Computation-free Newton’s Method . Unlike the classical Newton’s method, the proposed modification neither requires to compute and store the Jacobian matrix,nor to solve a system of linear equations in ea...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English English |
| Published: |
Euclidean Press, LLC
2010
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/15342/ http://psasir.upm.edu.my/id/eprint/15342/1/Jacobian%20computation-free%20Newton%27s%20method%20for%20systems%20of%20nonlinear%20equations..pdf |
| _version_ | 1848842650404257792 |
|---|---|
| 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 |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We propose a modification to Newton’s method for solving nonlinear equations,namely a Jacobian Computation-free Newton’s Method . Unlike the classical Newton’s
method, the proposed modification neither requires to compute and store the Jacobian matrix,nor to solve a system of linear equations in each iteration. This is made possible by approximating the Jacobian inverse to a diagonal matrix without computing the Jacobian. The
proposed method turns out to be significantly cheaper than Newton’s method, much faster than fixed Newton and is suitable for small, medium or large scale nonlinear equations with a dense or sparse Jacobian. After proving the convergence of the reported algorithm, numerical
experiments are reported to illustrate the promise of this method. |
| first_indexed | 2025-11-15T08:02:30Z |
| format | Article |
| id | upm-15342 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T08:02:30Z |
| publishDate | 2010 |
| publisher | Euclidean Press, LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-153422015-11-02T08:53:38Z http://psasir.upm.edu.my/id/eprint/15342/ Jacobian computation-free Newton's method for systems of nonlinear equations. Yusuf, Mohammed Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor We propose a modification to Newton’s method for solving nonlinear equations,namely a Jacobian Computation-free Newton’s Method . Unlike the classical Newton’s method, the proposed modification neither requires to compute and store the Jacobian matrix,nor to solve a system of linear equations in each iteration. This is made possible by approximating the Jacobian inverse to a diagonal matrix without computing the Jacobian. The proposed method turns out to be significantly cheaper than Newton’s method, much faster than fixed Newton and is suitable for small, medium or large scale nonlinear equations with a dense or sparse Jacobian. After proving the convergence of the reported algorithm, numerical experiments are reported to illustrate the promise of this method. Euclidean Press, LLC 2010 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/15342/1/Jacobian%20computation-free%20Newton%27s%20method%20for%20systems%20of%20nonlinear%20equations..pdf Yusuf, Mohammed Waziri and Leong, Wah June and Abu Hassan, Malik and Monsi, Mansor (2010) Jacobian computation-free Newton's method for systems of nonlinear equations. Journal of Numerical Mathematics and Stochastics, 2 (1). pp. 54-63. ISSN 2151-2302 English |
| spellingShingle | Yusuf, Mohammed Waziri Leong, Wah June Abu Hassan, Malik Monsi, Mansor Jacobian computation-free Newton's method for systems of nonlinear equations. |
| title | Jacobian computation-free Newton's method for systems of nonlinear equations. |
| title_full | Jacobian computation-free Newton's method for systems of nonlinear equations. |
| title_fullStr | Jacobian computation-free Newton's method for systems of nonlinear equations. |
| title_full_unstemmed | Jacobian computation-free Newton's method for systems of nonlinear equations. |
| title_short | Jacobian computation-free Newton's method for systems of nonlinear equations. |
| title_sort | jacobian computation-free newton's method for systems of nonlinear equations. |
| url | http://psasir.upm.edu.my/id/eprint/15342/ http://psasir.upm.edu.my/id/eprint/15342/1/Jacobian%20computation-free%20Newton%27s%20method%20for%20systems%20of%20nonlinear%20equations..pdf |