Title page for etd-0815106-153718


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URN etd-0815106-153718
Author Ho-Pu Chen
Author's Email Address No Public.
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Department Applied Mathematics
Year 2005
Semester 2
Degree Master
Type of Document
Language English
Title Radial Bases and Ill-Posed Problems
Date of Defense 2006-06-07
Page Count 101
Keyword
  • ill-posed problems
  • radial basis function
  • Abstract RBFs are useful in scientific computing. In this thesis, we are interested in the positions of collocation points and RBF centers which causes the matrix for RBF interpolation singular and ill-conditioned. We explore the best bases by minimizing error function in supremum norm and root mean squares. We also use radial basis function to interpolate shifted data and find the best basis in certain sense. 
    In the second part, we solve ill-posed problems by radial basis collocation method with different radial basis functions and various number of bases. If the solution is not unique, then the numerical solutions are different for different bases. To construct all the solutions, we can choose one approximation solution and add the linear combinations of the difference functions for various bases. If the solution does not exist, we show the numerical solution always fail to satisfy the origin equation.
    Advisory Committee
  • Zi-Cai Li - chair
  • Lee-van Ling - co-chair
  • Tz-Luen Horng - co-chair
  • Chien-Sen Huang - co-chair
  • Tzon-Tzer Lu - advisor
  • Files
  • etd-0815106-153718.pdf
  • indicate in-campus access immediately and off_campus access in a year
    Date of Submission 2006-08-15

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