In the present paper the optimal quadrature formulas in the sense of Sard are constructed for numerical integration of the integral $\int_a^b e^{ 2\pi i\omega x}\varphi(x)d x$ with $\omega\in \mathbb{ R}$ in the Hilbert space $W_2^{ (2,1)}[a,b]$ of complex-valued functions. Furthermore, the explicit expressions for coefficients of the constructed optimal quadrature formulas are obtained. At the end of the paper some numerical results are presented.
Categories: math.NA cs.NA math.CV