An application of tensor products of functionals in problems of numerical integration

N. Temirgaliev ; S. S. Kudaibergenov ; A. A. Shomanova

Izvestiya. Mathematics , Tome 73 (2009) no. 2, pp. 393-434.

Résumé

We introduce a new notion of tensor product of functionals and apply it to problems of numerical integration. We find the exact orders of the errors arising on various classes of functions, some of which are known and some are new.

Détail

Keywords: tensor products of functionals, numerical integration, Smolyak quadrature formulae, discrepancy, Korobov grid, number-theoretic methods, theory of divisors, Chebyshev system, recovery from inexact information.

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