Optimal algorithms theory and estimation with unknown but bounded errors

This paper deals with the theory of optimal algorithms for problems which cannot be solved exactly. The general purpose is the approximation, as good as possible in a minmax sense, of a given map of any function belonging to a given class, knowing only limited and error contaminated information about it. This theory gives interesting results in system parameter estimation, when no reliable statistical hypothesis on the involved functions and errors can be made, but only a bound of them is known. In particular the existence and the computation of linear optimal algorithms for this problem are investigated and the corresponding errors are evaluated.