A structured Broyden's-like method for solving systems of nonlinear equations
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| date | 2015-01-11 09:06:32 |
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| id | 11363 |
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| internalnotes | [1] E.D. Dolan, J.J. More, Benchmarking optimization software with perpormance profiles, Math. Program. 91 (2002) 201-213. [2] Dennis, J, E., 1983, Numerical methods for unconstrained optimization and nonlinear equations, Prince-Hall, Inc., Englewood Cliffs, New Jersey [3] C.G. Broyden A class of methods for solving nonlinear simultaneous equations, Math. Comput., 19 (1965), 577-593. [4] D.H. Li and M. Fukushima, A modified BFGS method and its global convergence in nonconvex minimization, J. Comput. Appl. Math. 129 (2001) 15-35. [5] Kelley, C. T. 1995. Iterative Methods for Linear and Nonlinear Equations. PA: SIAM, Philadelphia [6] Byeong, C. S. Darvishi, M. T. and Chang, H. K. 2010. A comparison of the Newton-Krylov method with high order Newton-like methods to solve nonlinear systems . Appl. Math. Comput. 217: 3190-3198. [7] J.E. Dennis Jr., H.J. Martinez, and R.A. Tapia, Convergence theory for the structured BFGS secant method with an application to nonlinear least squares, J. Optim. Theory Appl. 61 (1989), pp. 161-178. |
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| spelling | 11363 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=11363 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal UniSZA Unisza unisza image/jpeg inches 96 96 788 1426x788 1426 40 40 2015-01-11 09:06:32 5594-01-FH02-FIK-15-02361.jpg UniSZA Private Access A structured Broyden's-like method for solving systems of nonlinear equations Applied Mathematical Sciences We suggested a Broyden’s-Like method in which the Jacobian of the system has some special structure. In this approach, instead of approximating the whole Jacobian using the Broyden’s updating formula, we considered an update which only approximates part of the Jacobian matrix that is not easily attained. The anticipation has been to further improve the performance of Broyden’s scheme in which the Jacobian of the system has some special structure. The effectiveness of our proposed scheme is appraised through numerical comparison with some well known Newton’s-like methods. 8 141 HIKARI Ltd. HIKARI Ltd. 7039-7046 [1] E.D. Dolan, J.J. More, Benchmarking optimization software with perpormance profiles, Math. Program. 91 (2002) 201-213. [2] Dennis, J, E., 1983, Numerical methods for unconstrained optimization and nonlinear equations, Prince-Hall, Inc., Englewood Cliffs, New Jersey [3] C.G. Broyden A class of methods for solving nonlinear simultaneous equations, Math. Comput., 19 (1965), 577-593. [4] D.H. Li and M. Fukushima, A modified BFGS method and its global convergence in nonconvex minimization, J. Comput. Appl. Math. 129 (2001) 15-35. [5] Kelley, C. T. 1995. Iterative Methods for Linear and Nonlinear Equations. PA: SIAM, Philadelphia [6] Byeong, C. S. Darvishi, M. T. and Chang, H. K. 2010. A comparison of the Newton-Krylov method with high order Newton-like methods to solve nonlinear systems . Appl. Math. Comput. 217: 3190-3198. [7] J.E. Dennis Jr., H.J. Martinez, and R.A. Tapia, Convergence theory for the structured BFGS secant method with an application to nonlinear least squares, J. Optim. Theory Appl. 61 (1989), pp. 161-178. |
| spellingShingle | A structured Broyden's-like method for solving systems of nonlinear equations |
| summary | We suggested a Broyden’s-Like method in which the Jacobian of the system has some special structure. In this approach, instead of approximating the whole Jacobian using the Broyden’s updating formula, we considered an update which only approximates part of the Jacobian matrix that is not easily attained. The anticipation has been to further improve the performance of Broyden’s scheme in which the Jacobian of the system has some special structure. The effectiveness of our proposed scheme is appraised through numerical comparison with some well known Newton’s-like methods. |
| title | A structured Broyden's-like method for solving systems of nonlinear equations |
| title_full | A structured Broyden's-like method for solving systems of nonlinear equations |
| title_fullStr | A structured Broyden's-like method for solving systems of nonlinear equations |
| title_full_unstemmed | A structured Broyden's-like method for solving systems of nonlinear equations |
| title_short | A structured Broyden's-like method for solving systems of nonlinear equations |
| title_sort | structured broyden's-like method for solving systems of nonlinear equations |