Radial basis functions under tension
Radial basis function interpolation is one of the prime methods for interpolation to scattered data in more than one dimension. Both for application and for the theory, so-called native spaces associated with the radial basis functions are very important. In this paper, such spaces are defined and studied for radial basis functions with parameters (``tension parameters''). Using these semi-Hilbert spaces, properties of the splines under tension are studied in depth, for example error estimates in uniform norm. Also, several numerical examples using such splines under tension are provided.
conditionally positive definite functions
scientific article; zbMATH DE number 2086002