A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations
We suggest a conjugate gradient (CG) method for solving symmetric systems of nonlinear equations without computing Jacobian and gradient via the special structure of the underlying function. This derivative-free feature of the proposed method gives it advantage to solve relatively large-scale proble...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2015/961487 |
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| _version_ | 1850175534004174848 |
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| author | Mohammed Yusuf Waziri Jamilu Sabi’u |
| author_facet | Mohammed Yusuf Waziri Jamilu Sabi’u |
| author_sort | Mohammed Yusuf Waziri |
| collection | DOAJ |
| description | We suggest a conjugate gradient (CG) method for solving symmetric systems of nonlinear equations without computing Jacobian and gradient via the special structure of the underlying function. This derivative-free feature of the proposed method gives it advantage to solve relatively large-scale problems (500,000 variables) with lower storage requirement compared to some existing methods. Under appropriate conditions, the global convergence of our method is reported. Numerical results on some benchmark test problems show that the proposed method is practically effective. |
| format | Article |
| id | doaj-art-c00a24c92d1c4e3eac32289053e12161 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c00a24c92d1c4e3eac32289053e121612025-08-20T02:19:26ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252015-01-01201510.1155/2015/961487961487A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear EquationsMohammed Yusuf Waziri0Jamilu Sabi’u1Department of Mathematical Sciences, Faculty of Science, Bayero University Kano, Kano, NigeriaDepartment of Mathematics, Faculty of Science, Northwest University Kano, Kano, NigeriaWe suggest a conjugate gradient (CG) method for solving symmetric systems of nonlinear equations without computing Jacobian and gradient via the special structure of the underlying function. This derivative-free feature of the proposed method gives it advantage to solve relatively large-scale problems (500,000 variables) with lower storage requirement compared to some existing methods. Under appropriate conditions, the global convergence of our method is reported. Numerical results on some benchmark test problems show that the proposed method is practically effective.http://dx.doi.org/10.1155/2015/961487 |
| spellingShingle | Mohammed Yusuf Waziri Jamilu Sabi’u A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations International Journal of Mathematics and Mathematical Sciences |
| title | A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations |
| title_full | A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations |
| title_fullStr | A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations |
| title_full_unstemmed | A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations |
| title_short | A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations |
| title_sort | derivative free conjugate gradient method and its global convergence for solving symmetric nonlinear equations |
| url | http://dx.doi.org/10.1155/2015/961487 |
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