The complete C(N)D-solution of the proЫem recovery of functions from anisotropic Sobolev classes Ьу their unexact trigonometric Fourier coeffi.cients - Utessov А.В.; Abdykulov А.Т. (Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series, 2018)
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.