Multivariate Spline Functions.

Abstract : This report addresses various approaches to multidimensional splines including a partial survey of the literature. In the first section the combined case of interpolating and smoothing by the use of splines is presented. The second section presents a class of multivariate spline functions associated with a general partial differential operator defined on an appropriate Sobolev space. The third section addresses the tensor product of Ahlberg, Nilson, Walsh and the blending splines introduced by Gordon. (Author)