Optimal quadratures in the sense of Sard in a Hilbert space

An optimal quadrature formula in the sense of Sard in the Hilbert space K2(Pm)K2(Pm) is constructed. New optimal quadrature formula of such a type and explicit expressions for the corresponding optimal coefficients are obtained using S.L. Sobolev’s method. The obtained optimal quadrature formula is exact for the trigonometric functions sinωx,cosωxsinωx,cosωx, and for algebraic polynomials of degree m-3m-3. Finally, some numerical results for the norm of the error functional of the optimal quadrature formulas are presented.