Optimal quadrature formulas in the space W쐠2 (1,0) of periodic functions

Abstract

This paper is devoted to the process of constructing an optimal quadrature formula in the Hilbert space of real-valued, periodic functions. Here, in order to obtain the upper bound for the absolute error of the considered quadrature formula, the norm of the error functional is calculated. In the calculation of the norm of the error functional the extremal function of the quadrature formula is used. Further, the system of linear equations for coefficients of the quadrature formula that give the minimum value to the norm of the error functional is obtained.