The complete C(N)D-solution of the proЫem recovery of functions from anisotropic Sobolev classes Ьу their unexact trigonometric Fourier coeffi.cients


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Authors

  • А.В. Utessov Aktobe State Regional University named after K. Zhubanov
  • A. Abdykulov K. Zhubanov Aktobe Regional University

Keywords:

computational (numerical) diameter, anisotropic Sobolev class, limiting error, optimal computing unit, recovery Ьу unaccurate information, massive of limiting error

Abstract

In the case when numerical information is removed from the trigonometric
Fourier coefficients - one of the main linear functionals - K(B) is fully solvedN is the problem r of optimal recovery of functions from anisotropic classes
Sobolev 1w;i,··•,1 s (O, 1) • Exactly, the unimproved order du(O; FR )L2 :::::::
1
N-(r1 + ... +r; )- reconstructing functions from the exact values of their trigonometric
Fourier coefficients. Based on this, an optimal computing -1 -1 aggregate, -1 1 ( t + ... +r2 is a trigonometric polynomial and the value of EN = N- 1 s ) of the marginal error of calculating the Fourier coefficients is found, which preserves the unimproved
order of recovery from accurate information. Then it is shown that the computational
aggregates of recovery by trigonometric Fourier coefficients with the best
there is no (ordinal) error.

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Published

2018-03-30

How to Cite

Utessov А., & Abdykulov А. (2018). The complete C(N)D-solution of the proЫem recovery of functions from anisotropic Sobolev classes Ьу their unexact trigonometric Fourier coeffi.cients . Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, Computer Science, Mechanics Series, 122(1), 90–98. Retrieved from https://bulmathmc.enu.kz/index.php/main/article/view/20

Issue

Vol. 122 No. 1 (2018)

Section

Статьи