Approximation in L_p(R^d) from a space spanned by the scattered shifts of a radial basis function

A new multivariate approximation scheme on R^d using scattered translates of the "shifted" surface spline function is developed. The scheme is shown to provide spectral L_p-approximation orders with 1 ≤ p ≤ ∞, i.e., approximation orders that depend on the smoothness of the approximands. In addition, it applies to noisy data as well as noiseless data. A numerical example is presented with a comparison between the new scheme and the surface spline interpolation method.