CONSTRUCTION OF OPTIMAL QUADRATURE FORMULAS IN SOBOLEV SPACE.

In this article, a series of problems related to the creation and application of quadrature and cubature formulas, including: finding errors of quadrature and cubature formulas in the Gilbert phases of differential functions; calculating error functionals of found extremal functions using extremal functions; finding the conditions for the existence and uniqueness of optimal quadrature and cubature formulas; developing new algorithms for constructing discrete operators based on optimal quadrature formulas, as well as determining the optimal coefficient adjustments, are discussed.