Title page for etd-0726110-143212


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URN etd-0726110-143212
Author Wan-Wei Wang
Author's Email Address m972040005@student.nsysu.edu.tw
Statistics This thesis had been viewed 5101 times. Download 948 times.
Department Applied Mathematics
Year 2009
Semester 2
Degree Master
Type of Document
Language English
Title Effective Condition Number for Underdetermined Systems and its Application to Neumann Problems, Comparisons of Different Numerical Approaches
Date of Defense 2010-06-10
Page Count 75
Keyword
  • effective condition number
  • MFV
  • stability
  • convergence
  • underdetermined system
  • Abstract In this thesis, for the under-determined system Fx = b with the matrix
    F ∈m×n (m ≤ n), new error bounds involving the traditional condition number
    and the effective condition number are established. Such error bounds are
    simple than those of over-determined system. The errors results implies that
    for stability, the condition number and the effective condition numbers are
    important if the perturbation of matrix F and vector b are dominant, respectively.
    This thesis is also devoted to the application of Neumann problems,
    where the consistent condition holds to guarantee the existence of multiple
    solutions. For the traditional Neumann conditions, the discrete consistent
    condition has to be satisfied to guarantee the existence of numerical solutions.
    Such a discrete consistent condition can be removed, to greatly simplify the
    numerical algorithms, and to retain the same convergence rates. For Neumann
    Problems, we may solve its ordinal discrete linear equations, or the
    underdetermined systems by ignoring some dependent equations, or the fixed
    variables methods. Moreover, we may choose different equations to be ignored,
    and different variables to be fixed. The comparisons of these different
    methods and choices are important in applications. In this thesis, the new
    comparisons and relations of stability and accuracy are first explored, and
    some interesting results and new discoveries are found. Numerical examples
    of Neumann problem in 1D are carried out, to support the analysis made.
    However, the algorithms and stability analysis can be applied to the complicated
    Nuemann problems in 2D and 3D, such as the traction problems in
    linear elastic problems.
    Advisory Committee
  • Chien-Sen Huang - chair
  • Tzon-Tzer Lu - co-chair
  • Ming-Gong Lee - co-chair
  • none - co-chair
  • Zi-Cai Li - advisor
  • Files
  • etd-0726110-143212.pdf
  • indicate access worldwide
    Date of Submission 2010-07-26

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