Convergence properties of surface spline interpolation on finite uniform grids
by
Aurelian Bejancu
University of Cambridge, England

Consider interpolation via Duchon's ``surface splines'' at the vertices of a sequence of uniform grids of decreasing mesh-size over a given bounded domain. We will present two types of results concerning the accuracy of this procedure when the function whose values are interpolated is sufficiently smooth. First, we obtain estimates of the decay of the error over a fixed strictly interior compact subset of the given domain. Second, we assume that the support of the data function is a subset of the interior of the domain and we give uniform error estimates over the whole domain.

Date received: February 6, 1999