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A generalized discrepancy and quadrature error bound. (English) Zbl 0889.41025
Summary: An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case. This error bound takes the form of a product of two terms. One term, which depends only on the integrand, is defined as a generalized variation. The other term, which depends only on the quadrature rule, is defined as a generalized discrepancy. The generalized discrepancy is a figure of merit for quadrature rules and includes as special cases the $${\mathcal L}^p$$-star discrepancy and $$P_\alpha$$ that arises in the study of lattice rules.

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