Variational Methods for Interpolation , Particularly by Radial BasisFunctionsWill

In this paper we give an overview of the variational approach to interpolation. Our particular interest is in the theory of radial basis functions, which include natural splines as a special case. Our approach is expository, seeking to put into a general framework seemly disparate results. However, at the end of the paper we do provide some glimpses of new results.