A generalized discrepancy and quadrature error bound

作者：Fred J. Hickernell · 发表于：Mathematics of Computation · 年份：1998 · DOI：10.1090/s0025-5718-98-00894-1 · 被引用次数：728 · 研究领域：Mathematical Approximation and Integration、Mathematical functions and polynomials、Radiation Shielding Materials Analysis

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 L p {\mathcal L}^p -star discrepancy and P α P_\alpha that arises in the study of lattice rules.