Approximation properties of Sobolev splines and the construction of compactly supported equivalents (Q2878983)

Radial basis function approximations of functions and data are particularly successful means of approximating, especially in high dimensional ambient spaces. For this purpose, large classes of useful kernel (radial basis) functions are available such as multiquadrics and the better localised Gaussian or Poisson kernels (they are exponentially decaying) for instance. In this article, radial basis functions of compact support are constructed and their approximation properties with respect to approximands from typical Sobolev spaces are studied and analysed, especially for their asymptotic error behaviour and also when bandlimited approximations are employed.