CURVATURE BASED CHARACTERIZATION OF RADIAL BASIS FUNCTIONS: APPLICATION TO INTERPOLATION

Choosing the scale or shape parameter of radial basis functions (RBFs) is a well-documented but still an open problem in kernel-based methods. It common to tune it according applications, and plays crucial role both for accuracy stability method. In this paper, we first devise direct relation between RBFs their curvature at each point. This leads characterizing scalable unscalable ones. We prove that all lie -class which means point xj proportional to, where cj corresponding spatially variable xj. Some most commonly used are then characterized classified accordingly curvature. Then, fundamental theory plane curves helps us recover univariate from scattered data, by enforcing exact approximate solutions have same they meet. introducing curvature-based scaled with parameters depending on function values be approximated. Several numerical experiments devoted show method performs better than standard fixed-scale some other selection