Smoothness for Some Selected Test Functions Relative to Shape Parameter via IMQ

Abstract

Radial basis function (RBF) approximation has the potential to provide accurate func-tion approximations for large data site given at scattered node locations which yields smooth solutions for a given number of node points especially when the basis functions are scaled to be nearly at and when the shape parameter is choose wisely. In this paper, we concentrate on the choice of shape parameter, which must be choose wisely and the simplest strategy we adopt is to perform a series of interpolation experiments by varying the interval of shape parameter, and then pick the \best" one. The \best" was pick by checking the errors for different data sites and the smoothness of the error graphs. The results shows that the choice of interval for the shape parameter give better accuracy and smoothness of the graphs.