Geodesic
Best approximation methods and the order of informativeness of systems
Sbornik. Mathematics, Tome 39 (1981) no. 4, pp. 479-500 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] C. A. Micchelli, T. J. Rivlin, A survey of optimal recovery, Optimal estimation in approximation theory, Plenum Press, New York, 1977 | MR

[2] A. G. Marchuk, K. Yu. Osipenko, “Nailuchshee priblizhenie funktsii, zadannykh s pogreshnostyu v konechnom chisle tochek”, Matem. zametki, 17:3 (1975), 359–368 | MR | Zbl

[3] S. M. Nikolskii, “Priblizhenie funktsii trigonometricheskimi polinomami v srednem”, Izv. AN SSSR, seriya matem., 10 (1946), 207–256

[4] V. Ya. Arsenii, “Ob optimalnom summirovanii ryadov Fure s priblizhennymi koeffitsientami”, DAN SSSR, 183:2 (1968), 257–260