Date of Award

2009

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Committee Chairman, Dr Scott Sarra

Second Advisor

Committee member, Dr Ari Aluthge

Third Advisor

Committee member, Dr Basant Karna

Abstract

The Radial Basis Function (RBF) method is an important tool in the interpolation of multidimensional scattered data. The method has several important properties. One is the ability to handle sparse and scattered data points. Another property is its ability to interpolate in more than one dimension. Furthermore, the Radial Basis Function method provides phenomenal accuracy which has made it very popular in many fields. Some examples of applications using the RBF method are numerical solutions to partial differential equations, image processing, and cartography. This thesis involves researching Radial Basis Functions using different shape parameter strategies. First, we introduce the Radial Basis Function method by stating its history and development in Chapter 1. Second, we explain how Radial Basis Functions work in Chapter 2. Chapter 3 compares RBF interpolation to polynomial interpolation. Chapters 4 and 5 introduce the idea of variable shape parameters. In these chapters we compare and analyze the variable shape parameters in one and two dimensions. In Chapter 6, we introduce the challenges in interpolations due to errors in boundary regions. Here, we try to reduce the error using different shape parameter strategies. Chapter 7 lists the conclusions resulting from the research.

Subject(s)

Numerical analysis.

Mathematics.

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