A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations
We propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to im...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/348654 |
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| author | M. Y. Waziri W. J. Leong M. Mamat |
| author_facet | M. Y. Waziri W. J. Leong M. Mamat |
| author_sort | M. Y. Waziri |
| collection | DOAJ |
| description | We propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form. The numerical results verify that the proposed approach is a clear enhancement in numerical performance. |
| format | Article |
| id | doaj-art-35439682f2b04f2ab1552f23a382e2ea |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-35439682f2b04f2ab1552f23a382e2ea2025-02-03T01:07:50ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/348654348654A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear EquationsM. Y. Waziri0W. J. Leong1M. Mamat2Department of Mathematics, Faculty of Science, University Putra Malaysia, 43400 Serdang, MalaysiaDepartment of Mathematics, Faculty of Science, University Putra Malaysia, 43400 Serdang, MalaysiaDepartment of Mathematics, Faculty of Science and Technology, Malaysia Terengganu University, Kuala Lumpur 21030 Terengganu, MalaysiaWe propose an approach to enhance the performance of a diagonal variant of secant method for solving large-scale systems of nonlinear equations. In this approach, we consider diagonal secant method using data from two preceding steps rather than a single step derived using weak secant equation to improve the updated approximate Jacobian in diagonal form. The numerical results verify that the proposed approach is a clear enhancement in numerical performance.http://dx.doi.org/10.1155/2012/348654 |
| spellingShingle | M. Y. Waziri W. J. Leong M. Mamat A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations Journal of Applied Mathematics |
| title | A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations |
| title_full | A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations |
| title_fullStr | A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations |
| title_full_unstemmed | A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations |
| title_short | A Two-Step Matrix-Free Secant Method for Solving Large-Scale Systems of Nonlinear Equations |
| title_sort | two step matrix free secant method for solving large scale systems of nonlinear equations |
| url | http://dx.doi.org/10.1155/2012/348654 |
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