| URN |
etd-0706112-135542 |
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| Author |
Chao-Chun Cheng |
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| Author's Email Address |
No Public. |
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| Statistics |
This thesis had been viewed 5574 times. Download 1083 times. |
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| Department |
Applied Mathematics |
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| Year |
2011 |
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| Semester |
2 |
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| Degree |
Master |
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| Type of Document |
|
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| Language |
English |
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| Title |
Adaptive stepsize control in path tracking for total degree homotopy continuation method |
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| Date of Defense |
2012-06-28 |
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| Page Count |
68 |
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| Keyword |
continuation method
isolated solutions
polynomial equations
adaptive stepsize control
prediction and correction
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| Abstract |
The theory of solving polynomial systems by homotopy continuation method has been proposed by Garcia, Zangwill and Drexler, and the most typical method in this category is total degree homotpy. The numerical implementation of tracking homotopy curves can be taken as two parts: prediction and correction. In this thesis we compare the performance of several prediction methods in the total degree homotopy, including Runge-Kutta method, Adams-Bashforth method and cubic Hermite method. In addition, we design an adaptive stepsize control algorithm in path tracking, which is based on the information obtained during Newton correction process. The numerical experiment shows that the stepsize control algorithm is quite efficient and reliable in path tracking. In the end we employ the algorithm for solving eigenvalue problems by random product homotopy method |
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| Advisory Committee |
Tzon-Tzer Lu - chair
Chen-Chang Peng - co-chair
Hung-Tsai Huang - co-chair
Chien-Sen Huang - co-chair
Tsung-Lin Lee - advisor
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| Files |
indicate access worldwide |
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| Date of Submission |
2012-07-06 |
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