Full C(N)D–research of the problem of recovery functions from the generalized Sobolev class
In this paper a complete C(N)D-research of the problem of recovery functions from the generalized Sobolev class W^ω_r _2 is carried out in the case, where numerical information of volume N about the function f being restored is removed from linear functionals. Namely, firstly, the exact order of error of restoring functions from classes W^ω_r _2; is established in the metric L^q,2≤ q≤ ∞; secondly, a specific computing unit is proposed, that implements the exact order and its limiting error ε_N is found, that preserves the exact order and not improved in order; thirdly, it is proved that any computing unit constructed by the Fourier coefficients of the function being restored does not have a limiting error, better (in order) than ε_N. , number=4, journal=Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series, author=Utesov Адилжан, year=2023, month=Dec., pages=6–11