Generalised thin-plate splines and inverse-multiquadrics as radial basis functions for approximation.

Conferenciante: Martín Buhmann (Universidad Justuts-Liebig, Giessen)

Abstract: In theory and practice, thin-plate splines, multiquadrics, and inverse multiquadrics radial basis functions, turn out to be extremely useful kernels for interpolation and quasi-interpolation, in spite of their global support. This is because we can form linear combinations of them that reproduce high-order polynomials in any space dimension. This in turn provides high orders of convergence when sufficiently smooth functions are being approximated. In this talk we aim to generalise these kernels functions to avail users of larger choices of radial basis functions for practical applications.