A simple method for constructing almost interpolation sets in the case of existence of locally linearly independent systems of basis functions is presented. Various examples of such systems, including translates of box splines and nite-element splines, are considered.
A survey on some recent developments in multivariate interpolation , including characterizations of almost interpolation sets with respect to nite-dimensional spaces by conditions of Schoenberg-Whitney type, is given.
A characterization of almost interpolation conngurations of points in terms of supports of basis functions is presented. Moreover, we show that this characterization can be signiicantly simpliied in the case of existence of a locally linearly independent basis, so that almost interpolation sets can be constructed by taking a point in a support of each basis… (More)
In this paper we study problems of best L I-approximation to continuous functions from finite-dimensional subspaces under a variety of constraints. Included are problems of bounded coefficient approximation, approximation with interpolation, restricted range approximation, and restricted range and derivative approximation. Emphasis is placed on problems of… (More)