Title page for etd-0814111-210902


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URN etd-0814111-210902
Author Tzu-Yuan Lin
Author's Email Address No Public.
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Department Applied Mathematics
Year 2010
Semester 2
Degree Master
Type of Document
Language English
Title True Condition Number
Date of Defense 2011-06-16
Page Count 57
Keyword
  • functional approximation
  • stability analysis
  • effective condition number
  • true condition number
  • condition number
  • Abstract For linear system Ax = b, the traditional condition number is the worst case for all
    b’s and often overestimated in many problems. For a specific b, the effective condition
    number is a better upper bound for the relative error of x. But, it is also possible
    that this effective condition number is overestimated. In this thesis, we study the true
    ratio of the relative error of x to the relative perturbation of b, called the true condition
    number. We obtain several new upper bounds and estimates for true condition
    number. We also explore to change the system to an equivalent one by shifting b to
    minimize its effective condition number. Finally we apply all our results to functional
    approximation.
    Advisory Committee
  • Zi-Cai Li - chair
  • Tsung-Lin Lee - co-chair
  • Hung-Tsai Huang - co-chair
  • Chien-Sen Huang - co-chair
  • Tzon-Tzer Lu - advisor
  • Files
  • etd-0814111-210902.pdf
  • Indicate in-campus at 0 year and off-campus access at 1 year.
    Date of Submission 2011-08-14

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