Optimal recovery of functions from anisotropic Sobolev classes on a power – logarithmic scale
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DOI:
https://doi.org/10.32523/2616-7182Keywords:
computational (numerical) diameter, optimal recovery, computing unit, linear functional, exact order of the recovery errorAbstract
In this paper, within the framework of the С (N) D - formulation of the recovery problem, the problem
of optimal recovery of functions from anisotropic Sobolev classes in a power-logarithmic scale in the metric Lq
(2 ≤ q ≤
∞) is solved. Namely, in the case when the values l
(1)
N (f), ..., l(N)
N (f) of linear functionals l
(1)
N , ..., l(N)
N defined on the
considered functional class are used as numerical information about a function, firstly, the exact order of the recovery
error is established, and secondly, a specific computing unit ϕ¯N
¯l
(1)
N (f), ..., ¯l
(N)
N (f); ·
is indicated that implements the
established exact order.