Author(s)

Donald E. Myers

Abstract

Smoothing and interpolation with radial basis functions Donald E. Myers Department of Mathematics, University of Arizona, Tucson A Z, E-Mail: myers@math.arizona.edu 1 INTRODUCTION Smoothing and interpolation are two aspects of the problem of "fitting" a function to data. In some instances one has only smoothing, in others only interpolation and in others both smoothing and interpolation. We shall assume that interpolation means that the function values at a data location match the data values, this property is variously called perfect or exact. In many applications the function and perhaps even its form are unknown, i.e., there are no state equations and hence one must make some form of assumptions in order for the problem to be well-posed. Although we begin with an example where the data locations are in 1-space, we shall mostly consider the case of k-dimensional Euclidean space. There are at least two different objectives in fitting a function to data (as we shall see these are

Keywords