Geodesic
Best approximation methods and the order of informativeness of systems
Sbornik. Mathematics, Tome 39 (1981) no. 4, pp. 479-500

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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. 
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     author = {K. Yu. Osipenko},
     title = {Best approximation methods and the order of informativeness of systems},
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K. Yu. Osipenko. Best approximation methods and the order of informativeness of systems. Sbornik. Mathematics, Tome 39 (1981) no. 4, pp. 479-500. http://geodesic.mathdoc.fr/item/SM_1981_39_4_a3/