Optimal Recovery of Functions from Numerical Information on Them and Limiting Error of the Optimal Computing Unit

2022

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DOI 10.1134/s0001434622050108
Data confidence 70 medium
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Abstract

The article establishes the exact order of the optimal recovery error for functions in the anisotropic Sobolev class $$W_2^{\mathbf r}$$ for the case in which the values of linear functionals defined on the class $$W_2^{\mathbf r}$$ are used as numerical information about the function. The limiting error of the computing unit that realizes the exact order of recovery is found.