On the scattered data interpolation and approximation using radial basis functions

Abstract

Radial basis functions have proved very useful in computer graphicx and neutral networks and are growing in popularity for solving partial differential equations. A small shape parameter and a small fill distance are both desirable for accuracy, but both cause ill conditioned problems. The accuracy of RBFs meshless greatly depends on the user defined radial basis centers and the shape parameter. The researchers are confirmed that even when circumventing the ill conditioning of the system matrix there usually is a value of the shape parameter which results in optimal approximation errors. So it is necessary to find a strategy between the good accuracy and the well posed interpolation problem and therefore looks for a good balance between accuracy and stability.