A numerical study on inverse quadratic optimal shape parameter in interpolation problems

Abstract

The main purpose of this work is to shed more light into the inverse quadratic radial basis function (RBF) in the application of interpolation. This RBF contains a parameter that plays a crucial role in determining the final result quality. Five strategies of variable shape parameters are numerically investigated. Both types of node distribution; normally and scattered, are considered. It is discovered that good results can be obtained when using some strategies particularly in 1D problem. Challenges become appearing when dealing with 2D and deserves further study.