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1860796949580480512
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INTELEK Repository
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Online Access
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https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072
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2024-10-02 15:24
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Restricted Document
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10799
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UniSZA
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1. Bogle, I. and J. Perkins, A new sparsity preserving quasi-Newton update for solving nonlinear equations. SIAM Journal on Scientific and Statistical Computing, 1990. 11(4): p. 621-630. 2. Broyden, C.G., A class of methods for solving nonlinear simultaneous equations. Mathematics of Computation, 1965. 19(92): p. 577-593. 3. Dembo, R.S., S.C. Eisenstat, and T. Steihaug, Inexact newton methods. SIAM, J. Numer. Anal, 1982. 19(2): p. 400-408. 4. Dennis, J.R., On the convergence of Broydens method for nonlinear systems of equations. Mathematics of Computation, 1971. 25(115):559-567. 5. Griewank, A., Broyden Updating, the Good and the Bad! Documenta Mathematica, 2012. Extra volume ISMP: p. 301-315. 6. Natasa, K. and L. Zorna, Newton-like method with modification of the right�hand vector. Journal of Computational Mathematics, 2001. 71: p. 237-250. 7. A. Ramli, M.L. Abdullah, and M. Mamat, Broyden's method for solving fuzzy nonlinear equations. Advances in Fuzzy Systems, 2010. Art ID 763270, 6 pages. 8. K. Muhammad, M. Mamat, and M.Y. Waziri, A Broyden’s-like Method for solving systems of Nonlinear Equations, World Applied Sciences Journal , 2013, 21(Special Issue of Applied Math.):168-173 9. Roose, A., Test Examples of Systems of Nonlinear Equations: Version 3- 901990: Estonian Software and Computer Service Company 10. Schlenkrich, S., A. Griewank, and A. Walther, On the local convergence of adjoint Broyden methods. Mathematical programming, 2010. 121(2): p. 221- 247. 11. Shin, B.C., M. Darvishi, and C.H. Kim, A comparison of the Newton–Krylov method with high order Newton-like methods to solve nonlinear systems. Applied mathematics and computation, 2010. 217(7): p. 3190-3198. 12. Waziri, M., W. Leong, and M. Mamat, A two-step matrix-free secant method for solving large-scale systems of nonlinear equations. Journal of Applied Mathematics, 2012. Article ID 348654, 6 pages. 13. Waziri, M.Y., H. Aisha, and I. Saidu, A modified chord Newton method for High - Dimensional Algebraic Equation. ARPN Journal of Engineering and Applied Sciences, 2012. 7(4): p.385-388. 14. Weerakoon, S. and T. Fernando, A variant of Newton's method with accelerated third-order convergence. Applied Mathematics Letters, 2000. 13(8): p. 87.
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oai_dc
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https://intelek.unisza.edu.my/intelek/pages/view.php?ref=10799
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10799 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=10799 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal image/jpeg inches 96 96 2024-10-02 15:24 591 1341x591 1341 4930-01-FH02-FIK-14-00724.jpg UniSZA Private Access Trapezoidal broyden's method for solving systems of nonlinear equations Applied Mathematical Sciences We propose in this paper a Broyden- like method using the trapezoidal rule to solve system of nonlinear equations. A two point predictor- corrector approach was used, where the Broyden method is the predictor and the proposed method is the corrector. Numerical experiment carried out on some test problems with standard initial points has shown that the proposed method is very encouraging. 8 5 251-260 1. Bogle, I. and J. Perkins, A new sparsity preserving quasi-Newton update for solving nonlinear equations. SIAM Journal on Scientific and Statistical Computing, 1990. 11(4): p. 621-630. 2. Broyden, C.G., A class of methods for solving nonlinear simultaneous equations. Mathematics of Computation, 1965. 19(92): p. 577-593. 3. Dembo, R.S., S.C. Eisenstat, and T. Steihaug, Inexact newton methods. SIAM, J. Numer. Anal, 1982. 19(2): p. 400-408. 4. Dennis, J.R., On the convergence of Broydens method for nonlinear systems of equations. Mathematics of Computation, 1971. 25(115):559-567. 5. Griewank, A., Broyden Updating, the Good and the Bad! Documenta Mathematica, 2012. Extra volume ISMP: p. 301-315. 6. Natasa, K. and L. Zorna, Newton-like method with modification of the right�hand vector. Journal of Computational Mathematics, 2001. 71: p. 237-250. 7. A. Ramli, M.L. Abdullah, and M. Mamat, Broyden's method for solving fuzzy nonlinear equations. Advances in Fuzzy Systems, 2010. Art ID 763270, 6 pages. 8. K. Muhammad, M. Mamat, and M.Y. Waziri, A Broyden’s-like Method for solving systems of Nonlinear Equations, World Applied Sciences Journal , 2013, 21(Special Issue of Applied Math.):168-173 9. Roose, A., Test Examples of Systems of Nonlinear Equations: Version 3- 901990: Estonian Software and Computer Service Company 10. Schlenkrich, S., A. Griewank, and A. Walther, On the local convergence of adjoint Broyden methods. Mathematical programming, 2010. 121(2): p. 221- 247. 11. Shin, B.C., M. Darvishi, and C.H. Kim, A comparison of the Newton–Krylov method with high order Newton-like methods to solve nonlinear systems. Applied mathematics and computation, 2010. 217(7): p. 3190-3198. 12. Waziri, M., W. Leong, and M. Mamat, A two-step matrix-free secant method for solving large-scale systems of nonlinear equations. Journal of Applied Mathematics, 2012. Article ID 348654, 6 pages. 13. Waziri, M.Y., H. Aisha, and I. Saidu, A modified chord Newton method for High - Dimensional Algebraic Equation. ARPN Journal of Engineering and Applied Sciences, 2012. 7(4): p.385-388. 14. Weerakoon, S. and T. Fernando, A variant of Newton's method with accelerated third-order convergence. Applied Mathematics Letters, 2000. 13(8): p. 87.
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| spellingShingle |
Trapezoidal broyden's method for solving systems of nonlinear equations
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| summary |
We propose in this paper a Broyden- like method using the trapezoidal rule to solve system of nonlinear equations. A two point predictor- corrector approach was used, where the Broyden method is the predictor and the proposed method is the corrector. Numerical experiment carried out on some test problems with standard initial points has shown that the proposed method is very encouraging.
|
| title |
Trapezoidal broyden's method for solving systems of nonlinear equations
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| title_full |
Trapezoidal broyden's method for solving systems of nonlinear equations
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| title_fullStr |
Trapezoidal broyden's method for solving systems of nonlinear equations
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| title_full_unstemmed |
Trapezoidal broyden's method for solving systems of nonlinear equations
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| title_short |
Trapezoidal broyden's method for solving systems of nonlinear equations
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| title_sort |
trapezoidal broyden's method for solving systems of nonlinear equations
|