Construction of Optimal Quadrature Formula for Numerical Calculation of Fourier Coefficients in Sobolev Space L₂⁽¹⁾

Nurali D. Boltaev¹, Abdullo R. Hayotov^1, and Kholmat M. Shadimetov¹

¹Department of Comptational Methods, Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

Cite this paper:
Nurali D. Boltaev, Abdullo R. Hayotov and Kholmat M. Shadimetov. Construction of Optimal Quadrature Formula for Numerical Calculation of Fourier Coefficients in Sobolev Space L₂⁽¹⁾. American Journal of Numerical Analysis. 2016; 4(1):1-7. doi: 10.12691/ajna-4-1-1

Abstract

In the present paper the optimal quadrature formula for approximate evaluation of Fourier coefficients is constructed for functions of the space . At the same time the explicit formulas for optimal coefficients, which are very useful in applications, are obtained. The obtained formula is exact for constant. In particular, as consequences of the main result the new optimal quadrature formulas for approximate evaluation of integrals and are obtained. Furthermore, the order of convergence of the constructed optimal quadrature formula is studied.

Keywords:
optimal quadrature formula extremal function error functional hilbert space

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