An improved diagonal Jacobian approximation via a new quasi-Cauchy condition for solving large-scale systems of nonlinear equations
We present a new diagonal quasi-Newton update with an improved diagonal Jacobian approximation for solving large-scale systems of nonlinear equations. In this approach, the Jacobian approximation is derived based on the quasi-Cauchy condition. The anticipation has been to further improve the perform...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30184/ http://psasir.upm.edu.my/id/eprint/30184/1/An%20improved%20diagonal%20Jacobian%20approximation%20via%20a%20new%20quasi.pdf |
| _version_ | 1848846605510246400 |
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| author | Waziri, Mohammed Yusuf Abdul Majid, Zanariah |
| author_facet | Waziri, Mohammed Yusuf Abdul Majid, Zanariah |
| author_sort | Waziri, Mohammed Yusuf |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We present a new diagonal quasi-Newton update with an improved diagonal Jacobian approximation for solving large-scale systems of nonlinear equations. In this approach, the Jacobian approximation is derived based on the quasi-Cauchy condition. The anticipation has been to further improve the performance of diagonal updating, by modifying the quasi-Cauchy relation so as to carry some additional information from the functions. The effectiveness of our proposed scheme is appraised through numerical comparison with some well-known Newton-like methods. |
| first_indexed | 2025-11-15T09:05:22Z |
| format | Article |
| id | upm-30184 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:05:22Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-301842016-02-12T08:59:02Z http://psasir.upm.edu.my/id/eprint/30184/ An improved diagonal Jacobian approximation via a new quasi-Cauchy condition for solving large-scale systems of nonlinear equations Waziri, Mohammed Yusuf Abdul Majid, Zanariah We present a new diagonal quasi-Newton update with an improved diagonal Jacobian approximation for solving large-scale systems of nonlinear equations. In this approach, the Jacobian approximation is derived based on the quasi-Cauchy condition. The anticipation has been to further improve the performance of diagonal updating, by modifying the quasi-Cauchy relation so as to carry some additional information from the functions. The effectiveness of our proposed scheme is appraised through numerical comparison with some well-known Newton-like methods. Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30184/1/An%20improved%20diagonal%20Jacobian%20approximation%20via%20a%20new%20quasi.pdf Waziri, Mohammed Yusuf and Abdul Majid, Zanariah (2013) An improved diagonal Jacobian approximation via a new quasi-Cauchy condition for solving large-scale systems of nonlinear equations. Journal of Applied Mathematics, 2013. art. no. 875935. pp. 1-6. ISSN 1110-757X; ESSN:1687-0042 http://dx.doi.org/10.1155/2013/875935 10.1155/2013/875935 |
| spellingShingle | Waziri, Mohammed Yusuf Abdul Majid, Zanariah An improved diagonal Jacobian approximation via a new quasi-Cauchy condition for solving large-scale systems of nonlinear equations |
| title | An improved diagonal Jacobian approximation via a new quasi-Cauchy condition for solving large-scale systems of nonlinear equations |
| title_full | An improved diagonal Jacobian approximation via a new quasi-Cauchy condition for solving large-scale systems of nonlinear equations |
| title_fullStr | An improved diagonal Jacobian approximation via a new quasi-Cauchy condition for solving large-scale systems of nonlinear equations |
| title_full_unstemmed | An improved diagonal Jacobian approximation via a new quasi-Cauchy condition for solving large-scale systems of nonlinear equations |
| title_short | An improved diagonal Jacobian approximation via a new quasi-Cauchy condition for solving large-scale systems of nonlinear equations |
| title_sort | improved diagonal jacobian approximation via a new quasi-cauchy condition for solving large-scale systems of nonlinear equations |
| url | http://psasir.upm.edu.my/id/eprint/30184/ http://psasir.upm.edu.my/id/eprint/30184/ http://psasir.upm.edu.my/id/eprint/30184/ http://psasir.upm.edu.my/id/eprint/30184/1/An%20improved%20diagonal%20Jacobian%20approximation%20via%20a%20new%20quasi.pdf |