Solvability of Multivariate Interpolation by Radial or Related Functions Original Research Article

Let X be a linear space, and H a Hilbert space. Let N denote a set of n distinct points in X designated by x1, ..., xn (these points are called nodes). It is desired to interpolate arbitrary data on N by a function in the linear span of the n functions, [formula] where yk are n distinct points in X (called knots), Tv are linear maps from X to H, and Fν are some suitable univariate functions. In this paper, we discuss the solvability of this interpolation scheme. For the case in which the nodes and knots coincide, we give a convenient condition which is equivalent to the nonsingularity of the interpolation matrices. We obtain some sufficient conditions for the case in which the nodes and knots do not necessarily coincide.