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

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.