Optimal-By-Accuracy and Optimal-By-Order Cubature Formulae

Melnik, K.N. and Melnik, R.V.N.

Journal of Computational and Applied Mathematics. 147, 233--262, 2002


In this paper the problem of optimal integration for fast oscillatory functions of two variables is solved constructively in the case where a priori information is limited. The connection of this problem with the problem of optimal recovery of a function from interpolational classes is analysed using properties of majorants and minorants for these functional classes.