OPTIMAL QUADRATURE FORMULA OF THE HERMITE TYPE

Аннотация

In this work, we discuss the construction of derivative optimal quadrature formulas in the Sobolev space. We derive an analytical expression for an error functional norm and obtain a system of linear equations Winner-Hopf type by the coefficients using the method of Lagrange multipliers. Further, we apply the Sobolev method to get the analytical representation of the optimal coefficients. Using these coefficients, we calculate the norm of the error functional of the optimal quadrature formula in cases m=3 and m=4 in Sobolev L(m)(0,1) space. We verify 2 ourtheoretical conclusions with thehelpofnumerical experiments. Keywords: Error functional, extremal function, Sobolev space, optimal coefficients, optimal quadrature formula.