Multivariate interpolation and conditionally positive definite functions. (English) Zbl 0703.41008

This is an extension of Duchon’s theory. That is, the problem of interpolating numerical data at a finite number of points in a space is considered. The interpolants are linear combinations of translates of a prescribed function h. There exists a semi-norm if and only if h is conditionally positive definite. The error estimates are obtained in terms of this semi-norm. In this development certain features of Duchon’s theory are preserved but the use of Fourier analysis is completely avoided.


41A05 Interpolation in approximation theory
41A15 Spline approximation