An error analysis for radial basis function interpolation

Radial basis function interpolation refers to a method of interpolation which writes the interpolant to some given data as a linear combination of the translates of a single function and a low degree polynomial. We develop an error analysis which works well when the Fourier transform of has a pole of order 2m at the origin and a zero at 1 of order 2 . In case 0 m , we derive error estimates which ll in some gaps in the known theory; while in case m > we obtain previously unknown error estimates. In this latter case, we employ dilates of the function , where the dilation factor corresponds to the ll distance between the data points and the domain.