Optimal estimation of linear operators from inaccurate data: A second look

Abstract

This paper intends to re-examine some results and proofs given in a previous publication on optimal estimation under uncertainty. In a rather general setting we showed that regularization of an element of a linear space relative to a quadratic criterion and inaccurate linear observations is an optimal method for recovering a linear operator of that element. For this to be the case, the regularization parameter must be chosen with care. © 1993 J.C. Baltzer AG, Science Publishers.