  This paper addresses the problem of approximating a function of bounded
variation from its scattered data. Radial basis function(RBF) interpolation
methods are known to approximate only functions in their native spaces, and to
date, there has been no known proof that they can approximate functions outside
the native space associated with the particular RBF being used. In this paper,
we describe a scattered data interpolation method which can approximate any
function of bounded variation from its scattered data as the data points grow
dense. As the class of functions of bounded variation is a much wider class
than the native spaces of the RBF, this method provides a crucial advantage
over RBF interpolation methods.
