Multivariate Interpolation with Increasingly Flat Radial Basis Functions
Department of Applied Mathematics
Illinois Institute of Technology
We consider the problem of multivariate interpolation with radial basis functions consisting of a scaling parameter. In particular, we discuss the limit of interpolants by radial basis functions in $\R^d$ as the scaling parameter of the RBFs goes to zero, i.e., the RBFs become increasingly flat. We present that the limit is a polynomial interpolant when the RBF is infinitely smooth and a polyharmonic interpolant when the RBF is of finitely smoothness.