N. Temirgaliev, S. S. Kudaibergenov, A. A. Shomanova, “An application of tensor products of functionals in problems of numerical integration”, Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 2,Pages <nobr>183

This article is cited in 12 papers

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

N. Temirgaliev^a, S. S. Kudaibergenov^b, A. A. Shomanova^a

^a L. N. Gumilev Eurasian National University
^b M. O. Auezov South Kazakhstan State University

Abstract: 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.

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.

UDC: 517.5

MSC: Primary 65D30; Secondary 41A55

Received: 11.03.2005
Revised: 05.04.2008

DOI: 10.4213/im956