Date of Award

Spring 1-1-2011

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Applied Mathematics

First Advisor

Bengt Fornberg

Second Advisor

Natasha Flyer

Third Advisor

Jeffrey Fox

Abstract

We present here a new stable algorithm for the small ϵ (flat basis function) limit in Radial Basis Function interpolation. Based of of the successes of previous methods, such as RBF-QR, we extend to the 2-D non-periodic domain using the Gaussian basis function. This new method, RBF-GA, shows substantial improvement in accuracy and conditioning over the RBF-Direct method, and it is also easy to implement. The theory involved can readily be extended to higher numbers of dimensions.

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