Best approximation methods and the order of informativeness of systems

The problem of approximating a linear functional from approximate values of a system of functionals is considered. The concept of the order of informativeness of a system is introduced as the minimal number of functionals that can be retained without making the approximation error worse. For approximation with respect to an orthonormal system of functionals in a Hilbert space the order of informativeness, the best approximation method, and its error are determined.
Bibliography: 4 titles.