Open AccessApproximation Functionals and Their Application
Author(s) -
A. Yuri K. Dem’yanovich,
T. A. Safonova,
Andrey Terekhov
Publication year - 2021
Publication title -
wseas transactions on mathematics
Language(s) - English
Resource type - Journals
eISSN - 2224-2880
pISSN - 1109-2769
DOI - 10.37394/23206.2021.20.51
Subject(s) - trajectory , mathematics , approximation theory , minimax approximation algorithm , space (punctuation) , approximation algorithm , point (geometry) , work (physics) , linear approximation , spouge's approximation , muffin tin approximation , approximation error , mathematical analysis , mathematical optimization , computer science , physics , geometry , nonlinear system , quantum mechanics , operating system
The purpose of this work is to obtain local estimates, and to calculate the constants of approximation of smooth functions. To achieve this goal, the trajectory of functionals, the concept of an approximation families of functionals, the tape of the trajectory of functionals and the width of the tape are considered. For this, the concepts of approximation functionals and their trajectories in the conjugate space are introduced, and the concepts of the trajectory tape and the tape width at a given point are discussed. The resulting overall evaluation of the approximation is applied to multidimensional cases, namely, to approximations by the Courant and Zlamal elements.