On Power Functions and Error Estimates for Radial Basis Function Interpolation Original Research Article

This paper discusses approximation errors for interpolation in a variational setting which may be obtained from the analysis given by Golomb and Weinberger. We show how this analysis may be used to derive the power function estimate of the error as introduced by Schaback and Powell. A simple error tool for the power function is presented, which is similar to one appearing in the work of Madych and Nelson. It is then shown that this tool is adequate to reproducing the original error analysis presented by Duchon. An interesting consequence of our work is that no explicit use is made of the polynomial reproduction properties of the interpolation operator.