Borodachov S. Optimization of approximate integration on certain classes of univariate and multivariate functions

Sets of quadrature formulas for classes of univariate and multivariate functions ("pointwise", "interval", other types). Solving the problem of optimization of formulas of approximate integration which use various types of information for a number of classes of univariate and multivariate functions. We use general methods of extremal problems of approximation theory and theory of quadrature formulas, methods developed by Nikol'skiy, Kiefer, Korneychuk, Smolyak, Bakhvalov, Motornyi, Lygun, Zhensykbaev, Babenko, and general facts from functional analysis, function theory, convex analysis. Best quadrature formulas for classes of univariate and multivariate functions, monotone along every variable, or having a given majorant for the moduli of continuity or given constraints for the derivatives. The results are new and have theoretical application. They can also be used for computations and computer tomography.