A generalized discrepancy and quadrature error bound
A generalized discrepancy and quadrature error bound
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DOI：
10.1090/s0025-5718-98-00894-1
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发表时间：
1998-01-01
影响因子：
2
通讯作者：
Hickernell, FJ
中科院分区：
文献类型：
--
作者：
Hickernell, FJ
多维正交限制的误差将导出，其中包括Koksma-Hlawka不等式作为一种特殊情况。此错误绑定的形式为两个术语。一个仅取决于积分的术语被定义为广义变化。另一个术语仅取决于正交规则，被定义为广义差异。普遍的差异是正交规则的优点，包括特殊情况下，晶格规则研究中出现的L-P-Star差异和P-alpha。
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-star discrepancy and P-alpha that arises in the study of lattice rules.