Construction of the optimal quadrature formula in L2(2,0)(0, 1) space by Sobolev’s method

The paper studies Sard's problem on construction of optimal quadrature formula in the space L 2 ( 2 , 0 ) by Sobolev's method. This problem consists of two parts: first calculating the norm of the error functional and then finding the minimum of this norm by coefficients of quadrature formulas. Here the norm of the error functional is calculated with the help of the extremal function. Then using the method of Lagrange multipliers the system of linear equations for coefficients of the optimal quadrature formula in the space L 2 ( 2 , 0 ) is obtained. Further, Sobolev's method of construction of optimal quadrature formulas in the space L 2 ( 2 , 0 ) ⁠, which based on the discrete analogue D2[β ], is described. Finally, at the end of the paper the rate of convergence of the optimal quadrature formula in the space L 2 ( 2 , 0 ) is presented.

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