A generalized discrepancy and quadrature error bound

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 Lp-star discrepancy and Pα that arises in the study of lattice rules.

• Type: Journal
• Year: 1998
• Where: MOC
• Authors: Fred J. Hickernell
• Keywords: Generalized Discrepancy, MOC 1998, Multidimensional Quadrature, Special Cases