An error analysis for radial basis function interpolation

Summary. 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 of order 2. In case 0m, we derive error estimates which fill 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 fill distance between the data points and the domain.Mathematics Subject Classification (1991): 41A05, 41A25, 65D05, 41A63Revised version received December 17, 2003