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URN etd-0612113-133039
Author Hen-wen Chang
Author's Email Address No Public.
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Department Applied Mathematics
Year 2012
Semester 2
Degree Master
Type of Document
Language zh-TW.Big5 Chinese
Title The End Game Problem in Solving Algebraic Eigenvalue Problems by Homotopy Continuation Method
Date of Defense 2013-06-27
Page Count 42
Keyword
  • end game problem
  • eigenvalue problems
  • homotopy continuation
  • Abstract The homotopy continuation method is considered to solve polynomial systems. If the number of solutions of the starting system is much more than that of target system, many of curves will diverge when the homotopy parameter goes to the end. In this case we will have a difficulty in tracing the solution curves by continuation method because tracing divergent curves does not help us obtain any solution of target system but also its computation is very costly. As the parameter goes to the end, how to determine whether a curve converges or diverges effectively for reducing the computational cost is called the end game problem.
    In this thesis we will deal with the end game problem via the curve expression theory proposed by Morgan et al. The theory says the homotopy curve for solving polynomial systems can be expressed by Puiseux series expansion when the parameter is nearby the end. Moreover, the exponents of the leading term in Puiseux series determine the convergency of a curve. We also study the algebraic eigenvalue problems solving by homotopy continuation method. Several observations in numerical experiments for nonderogatory algebraic eigenvalue problem and its end game problem will be reported.
    Advisory Committee
  • Tzon-Tzer Lu - chair
  • Yueh-Cheng Kuo - co-chair
  • Hung-Tsai Huang - co-chair
  • Chieh-Sen Huang - co-chair
  • Tsung-Lin Lee - advisor
  • Files
  • etd-0612113-133039.pdf
  • Indicate in-campus at 1 year and off-campus access at 1 year.
    Date of Submission 2013-07-31

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