A Newton's-like method with extra updating strategy for solving singular fuzzy nonlinear equations
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| internalnotes | [1] Amira R., Mohad L. and Mustafa M., 2010, Broyden’s method for solving fuzzy nonlinear equations Advances in Fuzzy systems vol. 2010 ,6 pages. [2] Dennis, J, E., 1983, Numerical methods for unconstrained optimization and nonlinear equations, Prince-Hall, Inc., Englewood Cliffs, New Jersey [3] J.J. Buckley and Y. Qu, 1991, Solving fuzzy equations: a new solution concept, Fuzzy Sets and Systems 39, 291-301. [4] D. Dubois and H. Prade,, 1980, Fuzzy Sets and Systems: Theory and Application, Academic Press, New York. [5] J. Fang, 2002, On nonlinear equations for fuzzy mappings in probabilistic normed spaces, Fuzzy Sets and Systems 131, 357-364. [6] S. Abbasbandy and A. Jafarian, 2006, Steepest descent method for solving fuzzy nonlinear equations Applied Mathematics and Computation 174, 669- 675 [7] M.Y. Waziri and Z. A. Majid, 2012A new approach for solving dual Fuzzy nonlinear equations, Advances in Fuzzy Systems. Volume 2012, Article ID 682087, 5 pages doi:10.1155/2012/682087 no. 25, 1205 - 1217 [8] S. Abbasbandy and B. Asady, 2004, Newton’s method for solving fuzzy nonlinear equations, Appl. Math. Comput. 156 381-386. [9] J.J. Buckley and Y. Qu,, 1991, Solving systems of linear fuzzy equations, Fuzzy Sets Syst. 43, 33?. [10] M. Tavassoli Kajani , B. Asady and A. Hadi Venchehm, 2005, An iterative method for solving dual fuzzy nonlinear equations Applied Mathematics and Computation 167, 316-32 [11] R. Goetschel, W. Voxman, 1986, Elementary calculus, Fuzzy Sets and Systems 18 31?. [12] J. Fang, 2002, On nonlinear equations for fuzzy mappings in probabilistic normed spaces, Fuzzy Sets and Systems 131 357-364. J. Fang, On nonlinear equations for fuzzy mappings in probabilistic normed spaces, Fuzzy Sets and Systems 131 (2002) 357?4. [13] S.S.L. Chang, L.A. Zadeh, 1972,On fuzzy mapping and conterol, IEEE Transactions on Systems, Man and Cybernetics 2 30-34. [14] D. Dubois, H. Prade, 1978 Operations on fuzzy numbers, Journal of Systems Science 9 613- 626. [15] M. Mizumoto, K. Tanaka, 1976 The four operations of arithmetic on fuzzy numbers, Systems Computers and Controls 7 (5) 73-81. [16] J. Shokri, 1976 On Systems of Fuzzy Nonlinear Equations, Applied Mathematical Sciences, Vol. 2, 2008, no. 25, 1205 - 1217. |
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| spelling | 11360 https://intelek.unisza.edu.my/intelek/pages/view.php?ref=11360 https://intelek.unisza.edu.my/intelek/pages/search.php?search=!collection407072 Restricted Document Article Journal UniSZA Unisza unisza image/jpeg inches 96 96 1414 789 22 22 2015-01-11 09:03:05 1414x789 5591-01-FH02-FIK-15-02360.jpg UniSZA Private Access A Newton's-like method with extra updating strategy for solving singular fuzzy nonlinear equations Applied Mathematical Sciences The basic requirement of Newtons method in solving systems of nonlinear equations is, the Jacobian must be non-singular. Violating this condition, i.e. the Jacobian to be singular the convergence is too slow and may even be lost. This condition restricts to some extent the application of Newton method. In this paper we suggest a new approach for solving fuzzy nonlinear equations where the Jacobian is singular, via incorporating extra updating and restarting strategies in Newton’s method . The anticipation has been to bypass the point(s) in which the Jacobian is singular. Some numerical experiments have been reported, to show the efficiency of our approach and the results are compared with classical Newton’s method. 8 141 HIKARI Ltd. HIKARI Ltd. 7047-7057 [1] Amira R., Mohad L. and Mustafa M., 2010, Broyden’s method for solving fuzzy nonlinear equations Advances in Fuzzy systems vol. 2010 ,6 pages. [2] Dennis, J, E., 1983, Numerical methods for unconstrained optimization and nonlinear equations, Prince-Hall, Inc., Englewood Cliffs, New Jersey [3] J.J. Buckley and Y. Qu, 1991, Solving fuzzy equations: a new solution concept, Fuzzy Sets and Systems 39, 291-301. [4] D. Dubois and H. Prade,, 1980, Fuzzy Sets and Systems: Theory and Application, Academic Press, New York. [5] J. Fang, 2002, On nonlinear equations for fuzzy mappings in probabilistic normed spaces, Fuzzy Sets and Systems 131, 357-364. [6] S. Abbasbandy and A. Jafarian, 2006, Steepest descent method for solving fuzzy nonlinear equations Applied Mathematics and Computation 174, 669- 675 [7] M.Y. Waziri and Z. A. Majid, 2012A new approach for solving dual Fuzzy nonlinear equations, Advances in Fuzzy Systems. Volume 2012, Article ID 682087, 5 pages doi:10.1155/2012/682087 no. 25, 1205 - 1217 [8] S. Abbasbandy and B. Asady, 2004, Newton’s method for solving fuzzy nonlinear equations, Appl. Math. Comput. 156 381-386. [9] J.J. Buckley and Y. Qu,, 1991, Solving systems of linear fuzzy equations, Fuzzy Sets Syst. 43, 33?. [10] M. Tavassoli Kajani , B. Asady and A. Hadi Venchehm, 2005, An iterative method for solving dual fuzzy nonlinear equations Applied Mathematics and Computation 167, 316-32 [11] R. Goetschel, W. Voxman, 1986, Elementary calculus, Fuzzy Sets and Systems 18 31?. [12] J. Fang, 2002, On nonlinear equations for fuzzy mappings in probabilistic normed spaces, Fuzzy Sets and Systems 131 357-364. J. Fang, On nonlinear equations for fuzzy mappings in probabilistic normed spaces, Fuzzy Sets and Systems 131 (2002) 357?4. [13] S.S.L. Chang, L.A. Zadeh, 1972,On fuzzy mapping and conterol, IEEE Transactions on Systems, Man and Cybernetics 2 30-34. [14] D. Dubois, H. Prade, 1978 Operations on fuzzy numbers, Journal of Systems Science 9 613- 626. [15] M. Mizumoto, K. Tanaka, 1976 The four operations of arithmetic on fuzzy numbers, Systems Computers and Controls 7 (5) 73-81. [16] J. Shokri, 1976 On Systems of Fuzzy Nonlinear Equations, Applied Mathematical Sciences, Vol. 2, 2008, no. 25, 1205 - 1217. |
| spellingShingle | A Newton's-like method with extra updating strategy for solving singular fuzzy nonlinear equations |
| summary | The basic requirement of Newtons method in solving systems of nonlinear equations is, the Jacobian must be non-singular. Violating this condition, i.e. the Jacobian to be singular the convergence is too slow and may even be lost. This condition restricts to some extent the application of Newton method. In this paper we suggest a new approach for solving fuzzy nonlinear equations where the Jacobian is singular, via incorporating extra updating and restarting strategies in Newton’s method . The anticipation has been to bypass the point(s) in which the Jacobian is singular. Some numerical experiments have been reported, to show the efficiency of our approach and the results are compared with classical Newton’s method. |
| title | A Newton's-like method with extra updating strategy for solving singular fuzzy nonlinear equations |
| title_full | A Newton's-like method with extra updating strategy for solving singular fuzzy nonlinear equations |
| title_fullStr | A Newton's-like method with extra updating strategy for solving singular fuzzy nonlinear equations |
| title_full_unstemmed | A Newton's-like method with extra updating strategy for solving singular fuzzy nonlinear equations |
| title_short | A Newton's-like method with extra updating strategy for solving singular fuzzy nonlinear equations |
| title_sort | newton's-like method with extra updating strategy for solving singular fuzzy nonlinear equations |