Full C(N)D–research of the problem of recovery functions from the generalized Sobolev class


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Authors

  • Adilzhan Utesov ARU Zhubanova

DOI:

https://doi.org/10.32523/2616-7182/bulmathenu.2023/4.1

Keywords:

C(N)D-research, linear functional, computing unit, exact order of error of restoring, generalized Sobolev class, limiting error

Abstract

In this paper a complete C(N)D-research of the problem of recovery functions from the generalized Sobolev class $W^{\omega_{r}}_{2}$ is carried out in the case, where numerical information of volume $N$ about the function $f$ being restored is removed from linear functionals. Namely, firstly, the exact order of error of restoring functions from classes $W^{\omega_{r}}_{2};$ is established in the metric $L^{q},2\leq q\leq \infty;$ secondly, a specific computing unit is proposed, that implements the exact order and its limiting error $\bar{\varepsilon}_{N}$ is found, that preserves the exact order and not improved in order; thirdly, it is proved that any computing unit constructed by the Fourier coefficients of the function being restored does not have a limiting error, better (in order) than $\bar{\varepsilon}_{N}.$

Published

2023-12-30

How to Cite

Utesov А. (2023). Full C(N)D–research of the problem of recovery functions from the generalized Sobolev class. Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, Computer Science, Mechanics Series, 145(4), 6–11. https://doi.org/10.32523/2616-7182/bulmathenu.2023/4.1

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