Optimal quadrature formulas with derivatives in a periodic space

The paper is devoted to investigation of optimal formulas for approximate integration with derivatives in the Sobolev space L2(m)˜(0,1) of periodic functions. Here the extremal function for quadrature formulas of Hermite type is obtained. Applying this extremal function the square of the norm for the error functional of the considered Hermite type quadrature formulas is calculated. It is obtained the system of linear algebraic equations minimizing the norm of the error functional by coefficients of the quadrature formulas. Furthermore, here, Ivo Babuška’s theorem on zeros of extremal functions for quadrature formulas is generalized.

Hali tarjima qilinmagan