INEQUALITY OF THE BEST ANGULAR APPROXIMATION

The aim of the study is to analyze the best angular approximations of functions of many variables and to estimate these approximations from above. This allows one to better understand the applicability limits of these methods and optimize their use in problems of mathematical modeling and data analysis. In this paper, the properties of functions of several variables were studied and approaches to their approximation using angular approximations were proposed. Generalized Liouville–Weyl derivatives, which are used instead of classical mixed Weyl derivatives, are considered. The concept of general monotone sequences plays an important role in the study. The methodology includes the use of functional analysis, approximation theory, and analysis of parameters affecting the accuracy of approximation. The main results of the work are to obtain upper bounds for angular approximations for generalized Liouville–Weyl derivatives depending on the characteristics of the approximated functions. The results obtained are of interest to theorists working in the field of multivariate data analysis and mathematical modeling. The topic discussed in the article is closely related to the articles by A.A. Konyushkov, S.B. Stechkin, M.F. Timan, M.K. Potapova, B. Simonov, S. Tikhonov.