The extremal function of the optimal quadrature formula with derivative: The extremal function of the optimal quadrature formula with derivative - Khayriev, U.N; Nutfullaeva , A.Kh.; Barraeva, S.Sh. (MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS, 2024)
Abstract. This work is devoted to the process of constructing an optimal quadrature formula with derivative in the sense of Sard in the Hilbert space of periodic and complex-valued functions for numerical calculation of Fourier integrals. Here a quadrature sum consists of a linear combination of the given function value on a uniform mesh. The error of a quadrature formula is estimated from above by the functional norm of the error based on the Cauchy-Schwarz inequality. To calculate the norm, the concept of an extremal function is used. The extremal function corresponding to the error functional is found using the Riesz representation theorem.