ON OPTIMAL INTEGRATION OF FUNCTIONS BY THEIR INEXACT VALUES - Utessov А.Б. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2022)
One of the main concepts of the sections of mathematics called «Numerical Analysis» and «Approximation Theory» is the concept of " diameter". Depending on the goals set, various diameters are considered. In this work, in the context of the Сomputational (numerical) diameter, aimed at finding the best computing units for implementation on computers, the problem of optimal integration of functions from the multidimensional 1-periodic anisotropic Sobolev class is studied. Namely, when the values ​​of the function under consideration at a finite number of points act as numerical information, firstly, the exact order of the optimal integration error is established and a specific computing unit is written that implements the established exact order; secondly, the limit error of a specific optimal computing unit was found; thirdly, it has been proved that any computing unit constructed from the values ​​of the function at a finite number of points does not have a better (in order) limit error than the limit error of the specific computing unit written out.