An Optimal Quadrature Formula with Derivative in a Hilbert Space: An Optimal Quadrature Formula with Derivative in a Hilbert Space - Hayotov А.R.; Babaev, S.S. (MODERN PROBLEMS AND PROSPECTS OF APPLIED MATHEMATICS, 2024)
This article presents the derivation and analysis of a weighted optimal quadrature formula in the Hilbert space (2,1) 2 W (0,1) . The quadrature formula is expressed as a linear combination of function values and their first-order derivatives at equidistant nodes in the interval [0,1] .The coefficients are determined by minimizing the norm of the error functional in the dual space (2,1)* 2 W (0,1) , which measures the difference between the integral of a function over the interval and the quadrature approximation. Key results include explicit expressions for the coefficients and the norm of the error functional