N. Kh. Mamatova, A. R. Hayotov, Kh. M. Shadimetov, “Construction of optimal grid interpolation formulas in Sobolev space $\widetilde{L_2^m}(H)$ of periodic function of $n$ variables by Sobolev method”, Ufimsk. Mat. Zh., 2013, Volume 5, Issue 1,Pages 90

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Construction of optimal grid interpolation formulas in Sobolev space $\widetilde{L_2^m}(H)$ of periodic function of $n$ variables by Sobolev method

N. Kh. Mamatova, A. R. Hayotov, Kh. M. Shadimetov

Institute for Mathematics and Information Technologies of the National Academy of Sciences of Uzbekistan

Abstract: In the present work we consider the problem of constructing optimal grid interpolation formulas in the space $\widetilde{L_2^m}(H)$ of periodic function of $n$ variables. We find the coefficients of grid interpolation formulas.

Keywords: Sobolev space, optimal interpolation formula, properties of the discrete analogue of the operator $\Delta^m$, optimal coefficients.

UDC: 519.65

Received: 20.12.2011