Smoothing and Interpolation in a Convex Subset of a Hilbert Space

Interpolation and smoothing subject to convex constraints is considered. We clarify instances in a Hilbert space when the problem of finding the least norm solution to these problems can be separated into first finding the orthogonal projection onto the constraint set and then fitting the interpolation or smoothing requirements by solving a finite dimensional dual extremal problem. We report on some numerical experiments with this approach for a problem in EXAFS spectroscopy and also relate our results to special cases studied by others.