SIAM Undergraduate Research Online
Volume 4
In This Volume

Choosing Basis Functions and Shape Parameters for Radial Basis Function Methods
Published electronically December 2, 2011DOI: 10.1137/11S010840
Authors
Michael Mongillo (Illinois Institute of Technology)
Project Advisors
Greg Fasshauer (Illinois Institute of Technology)
Abstract
Radial basis function (RBF) methods have broad applications in numerical analysis and statistics. They have found uses in the numerical solution of PDEs, data mining, machine learning, and kriging methods in statistics. This work examines the use of radial basis functions in scattered data approximation. In particular, the experiments in this paper test the properties of shape parameters in RBF methods, as well as methods for finding an optimal shape parameter. Locating an optimal shape parameter is a difficult problem and a topic of current research. Some experiments also consider whether the same methods can be applied to the more general problem of selecting basis functions.

European Option Pricing Using a Combined Inverse Congruential Generator
Published electronically November 28, 2011 
Understanding the Impact Of Boundary and Initial Condition Errors on the Solution to a Thermal Diffusivity Inverse Problem
Published electronically November 18, 2011 
Interval Estimates for Predictive Values in Diagnostic Testing with Three Outcomes
Published electronically November 17, 2011 
Analysis of a CoEpidemic Model
Published electronically November 15, 2011 
Moody's Mega Math Challenge 2011 Champion PaperColorado River Water: Good to the Last AcreFoot
Published electronically November 11, 2011 
Computational Methods for a OneDimensional Plasma Model with Transport Field
Published electronically August 18, 2011 
Attractors: Nonstrange to Chaotic
Published electronically June 21, 2011 
Macroscopic CrossDiffusion Models Derived from Spatially Discrete Continuous Time Microscopic Models
Published electronically May 12, 2011 
On Numerical Methods for Elliptic Transmission Eigenvalue Problems
Published electronically March 4, 2011 
Parameter Estimation in Differential Equations: A Numerical Study of Shooting Methods
Published electronically February 23, 2011 
Spectral Clustering and Visualization: A Novel Clustering of Fisher's Iris Data Set
Published electronically February 23, 2011
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