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Radial Bases and Ill-Posed Problems

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.

Identiferoai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0815106-153718
Date15 August 2006
CreatorsChen, Ho-Pu
ContributorsTz-Luen Horng, Chien-Sen Huang, Lee-van Ling, Zi-Cai Li, Tzon-Tzer Lu
PublisherNSYSU
Source SetsNSYSU Electronic Thesis and Dissertation Archive
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0815106-153718
Rightsoff_campus_withheld, Copyright information available at source archive

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