LIMITING ERROR OF THE OPTIMAL COMPUTING UNIT FOR FUNCTIONS FROM THE CLASS Wr;α 2

Abstract

In the problem of optimal recovery of an infinite object (functions on a continuum, integrals of continuous functions, solutions of partial differential equations, derivative of functions,...) from finite numerical information about it, the problem of finding the limiting error of the optimal computing unit naturally arises, since the numerical information about the infinite object to be restored , as a rule, will not be accurate. In this article, the limiting error of the optimal computing unit is found in the problem of optimal recovery of periodic functions of many variables from the anisotropic Sobolev class  in a power-logarithmic scale in the space metric  The actuality of this work is determined by the following factors: firstly, the found limiting error of the optimal computing unit preserves the exact order of the smallest recovery error , when replacing exact numerical information about a function with inaccurate information and is unimprovable in order; secondly, the problem of finding the limiting error of an optimal computing unit has not previously been studied in the class under consideration; thirdly, the anisotropic Sobolev class in the power-logarithmic scale is a finer scale of classification of periodic functions according to the rate of decrease of their trigonometric Fourier coefficients than the anisotropic Sobolev class in the power scale.