Recent developments in error estimates for scattered-data interpolation via radial basis functions

Error estimates for scattered data interpolation by “shifts” of a positive definite function for target functions in the associated reproducing kernel Hilbert space (RKHS) have been known for a long time. However, apart from special cases where data is gridded, these interpolation estimates do not apply when the target functions generating the data are outside of the associated RKHS, and in fact until very recently no estimates were known in such situations. In this paper, we review these estimates in cases where the underlying space is Rn and the positive definite functions are radial basis functions (RBFs).