OPTIMAL FILTERING FOR THE BACKWARD HEAT-EQUATION

For the backward heat equation, stabilized by an a priori initial boun d, an estimator is determined for intermediate values that is optimal with respect to the bound and the observation accuracy. It is shown ho w this may be implemented computationally with error estimates for the computed approximation which can be made arbitrarily close to the unc ertainty level induced by the ill-posedness of the underlying problem. Thus, the feasibility of this for practical computation, inevitably s everely limited by that inherent uncertainty, is as good as possible.