Solving Nonlinear Algebraic Problem Using Newton Homotopy Differential Equation
This paper presents an efficient algorithm for solving a nonlinear equation. In our algorithm, the nonlinear system f (x) = 0 is solved by a homotopy method, in which a homotopy H (x,t) = f (x)-(1-t) f (x0) is introduced and the solution path of H(x, t) = 0 is followed from an obvious solution (x0,0...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
INSI Publications
2011
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/143/1/56-59.pdf http://irep.iium.edu.my/143/ http://www.insipub.com/ajbas/2011/56-59.pdf |
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| Summary: | This paper presents an efficient algorithm for solving a nonlinear equation. In our algorithm, the nonlinear system f (x) = 0 is solved by a homotopy method, in which a homotopy H (x,t) = f (x)-(1-t) f (x0) is introduced and the solution path of H(x, t) = 0 is followed from an obvious solution (x0,0)to the solution (x*,1) which we seek. An ordinary differential equation based on Newton homotopy
is used for following the solution path. Our homotop algorithm is much more efficient than the conventional iterations type algorithms. Some numerical examples are given in order to demonstrate the effectiveness. |
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