On the Error in Surface Spline Interpolation of a Compactly Supported Function

@inproceedings{Johnson1998OnTE,
title={On the Error in Surface Spline Interpolation of a Compactly Supported Function},
author={Michael J. Johnson},
year={1998}
}

We show that the Lp( )-norm of the error in surface spline interpolation of a compactly supported function in the Sobolev space W 2m 2 decays like O( p) where p := minfm;m+ d=p d=2g and m is a parameter related to the smoothness of the surface spline. In case 1 p 2, the achieved rate of O( ) matches that of the error when the domain is all of R and the interpolation points form an in nite grid.