Solvability of multivariate interpolation by radial or related functions
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.
Sun, X. P. "Solvability of multivariate interpolation by radial or related functions." Journal of approximation theory 72, no. 3 (1993): 252-267.
Journal of Approximation Theory