Radial basis functions of compact support
by
M.D. Buhmann
University of Dortmund

In this talk, radial basis functions that are compactly supported and give rise to positive definite interpolation matrices are discussed. There are some restrictions on the dimensionality of the problem (in all cases, an upper bound on the dimension n has to be met), which should be contrasted to the well-known cases such as multiquadric interpolation when there is no such bound. The particular advantage of radial basis functions of compact support, however, is the straightforward solvability of the linear systems that lead to the coefficients, because matrices are banded even when there are large numbers of data. They resemble the finite elements that are used for solving partial differential equations.

Several approaches to compactly supported radial functions are reviewed (for example the piecewise polynomial ones of Wendland and some others that are closely related to the thin-plate spline radial function) and some new classes of radial basis functions with compact support are given.

Date received: February 9, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabp-32.