Abstract
Surface spline interpolation when the domain is all of R d is known to converge much faster to the data function f than in the case when the domain is the unit ball. This difference is understood to be due to boundary effects which, as will be shown, also affect the size of the surface spline's coefficients. We propose a modified form of surface spline interpolation which, to a great extent, overcomes these boundary effects. This modified surface spline interpolant uses only the values of f at the given interpolation points.
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