EXACT ORDERS OF FUNCTION RECOVERY FROM INACCURATE DATA IN THE UNIFORM METRIC AND THE LIMITING ERROR OF INACCURATE INFORMATION

Abstract

This paper considers the problem of recovering multivariate functions from SW^r₂(0,1)^s Sobolev classes with dominating mixed derivative in the uniform metric L^∞(0,1)^s based on inaccurate information. The aim of this work is to investigate the accuracy of recovering functions from the considered class based on a finite number of linear functionals determined by a finite amount of inaccurate information in the form of Fourier coefficients, as well as to determine the optimal error of the inaccurate information for an optimal computational aggregate and to establish its massiveness. The study is carried out in the context of the problem of Computational (Numerical) Diameter. As a result of the research, exact orders of recovery of functions from Sobolev classes with dominating mixed derivative in the uniform metric from inaccurate data are obtained, and an optimal computational aggregate is constructed. The limiting error of inaccurate information for the constructed computational aggregate is found, and a set of computational aggregates has been constructed such that their limiting errors do not exceed the limiting error of the given aggregate, that is, the massiveness of the limiting error is determined. The obtained theoretical results are confirmed by numerical experiments. All of the above constitutes the scientific novelty of this work.

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