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Bulletin of the Abai KazNPU, the series of "Physical and Mathematical Sciences"

ON OPTIMAL RECOVERY OF FUNCTIONS FROM THE KOROBOV CLASS IN THE FRAMEWORK OF C(N)D – STATEMENT

Published June 2020
Aktobe Regional State University named after K. Zhubanov, Aktobe
Abstract

With optimal recovery of an operator T mapping a functional class F into a normed space Y by computing units constructed from inaccurate numerical information  l(N), the problems С(N)D - 1, С(N)D –2 and С(N)D –3 are successively solved. In this work, when we consider the unit operator as the operator T , the multidimensional oneperiodic Korobov class as the class F , the normalized space of functions continuous on the unit cube as the space Y , the trigonometric Fourier coefficients of the function being restored as numerical information  l(N) , problems С(N)D – 2 and С(N)D –3 are solved. Namely, in the problem С(N)D – 2 the marginal error of the optimal computing unit $$\left(\overline{l}^{\left(N\right)},\:\overline{\phi }_N\right)$$  from the previously solved problem С(N)D - 1 was found, and in the problem С(N)D - 3 it was proved, that any computing unit with respect to trigonometric Fourier coefficients has a better marginal error, than a computing unit $$\left(\overline{l}^{\left(N\right)},\:\overline{\phi }_N\right)$$

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How to Cite

[1]
Утесов , А. 2020. ON OPTIMAL RECOVERY OF FUNCTIONS FROM THE KOROBOV CLASS IN THE FRAMEWORK OF C(N)D – STATEMENT . Bulletin of the Abai KazNPU, the series of "Physical and Mathematical Sciences". 70, 2 (Jun. 2020), 129–135. DOI:https://doi.org/10.51889/2020-2.1728-7901.19 .