### Title page for etd-0726110-143212

URN etd-0726110-143212 Wan-Wei Wang m972040005@student.nsysu.edu.tw This thesis had been viewed 5203 times. Download 1009 times. Applied Mathematics 2009 2 Master English Effective Condition Number for Underdetermined Systems and its Application to Neumann Problems, Comparisons of Different Numerical Approaches 2010-06-10 75 effective condition number MFV stability convergence underdetermined system In this thesis, for the under-determined system Fx = b with the matrixF ∈m×n (m ≤ n), new error bounds involving the traditional condition numberand the effective condition number are established. Such error bounds aresimple than those of over-determined system. The errors results implies thatfor stability, the condition number and the effective condition numbers areimportant 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 multiplesolutions. For the traditional Neumann conditions, the discrete consistentcondition has to be satisfied to guarantee the existence of numerical solutions.Such a discrete consistent condition can be removed, to greatly simplify thenumerical algorithms, and to retain the same convergence rates. For NeumannProblems, we may solve its ordinal discrete linear equations, or theunderdetermined systems by ignoring some dependent equations, or the fixedvariables methods. Moreover, we may choose different equations to be ignored,and different variables to be fixed. The comparisons of these differentmethods and choices are important in applications. In this thesis, the newcomparisons and relations of stability and accuracy are first explored, andsome interesting results and new discoveries are found. Numerical examplesof Neumann problem in 1D are carried out, to support the analysis made.However, the algorithms and stability analysis can be applied to the complicatedNuemann problems in 2D and 3D, such as the traction problems inlinear elastic problems. Chien-Sen Huang - chair Tzon-Tzer Lu - co-chair Ming-Gong Lee - co-chair none - co-chair Zi-Cai Li - advisor indicate access worldwide 2010-07-26

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