Construction of an Optimal Quadrature Formula in the Hilbert Space of Periodic Functions

Abstract

This paper is devoted to constructing a new optimal quadrature formula in the Gilbert space of real-valued, periodic functions. Here, the norm of the error functional is calculated to obtain the upper bound for the absolute error of the considered quadrature formula. For this the extremal function of the quadrature formula is used. As well, optimal coefficients of the quadrature formula that give the minimum value to the norm of the error functional are found, and the norm of the error functional for the optimal quadrature formula is calculated. It is shown that the value of the norm of the found error functional is less than the value of the norm of the error functional for the constructed optimal quadrature formula in the space $$\widetilde{L_{2}}^{(1)}$$ .