Title page for etd-0706112-135542


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URN etd-0706112-135542
Author Chao-Chun Cheng
Author's Email Address No Public.
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Department Applied Mathematics
Year 2011
Semester 2
Degree Master
Type of Document
Language English
Title Adaptive stepsize control in path tracking for total degree homotopy continuation method
Date of Defense 2012-06-28
Page Count 68
Keyword
  • continuation method
  • isolated solutions
  • polynomial equations
  • adaptive stepsize control
  • prediction and correction
  • 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
    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
  • Files
  • etd-0706112-135542.pdf
  • indicate access worldwide
    Date of Submission 2012-07-06

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