L Auslander, E Feig, et al.
Advances in Applied Mathematics
Paper
The optimal recovery of smooth functions
Abstract
It is shown that there is a positive lower bound, c, to the uniform error in any scheme designed to recover all functions of a certain smoothness from their values at a fixed finite set of points. This lower bound is essentially attained by interpolation at the points by splines with canonical knots. Estimates of c are also given. © 1976 Springer-Verlag.