Solvability of multivariate interpolation by radial or related functions

Abstract

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.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1006/jath.1993.1020

Publication Date

1-1-1993

Journal Title

Journal of Approximation Theory

Link to Full Text

Share

COinS