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	The strong tractability of multivariate integration using lattice rules
	Hickernell, FJ ; Sloan, IH ; Wasilkowski, GW
	2004
关键词	BY-COMPONENT CONSTRUCTION WEIGHTED SOBOLEV SPACES QUADRATURE ACHIEVE
英文摘要	Although many applications involve integrals over unbounded domains, most of the theory for numerical approximation of integrals assumes that the integration domain is bounded. This article builds upon previous work by the authors that investigates the approximation of integrals over boxes that may be finite, semi-infinite or infinite in each coordinate direction. The integrand is sampled over a design, {W-1(z(i))}, that is a transformation of the nodeset of an integration lattice {z(i)}. The error bound for the numerical integration rule is shown to be a product of two terms: i) the discrepancy of the original design, {z(i)}, on the unit cube and ii) the variation of the integrand. Previously known convergence rates for extensible lattice rules on unit cubes are used to derive sufficient conditions for the strong tractability of integration over more general domains. The variation of the integrand depends on several factors, including the function W used to make the transformation of variables.; Computer Science, Interdisciplinary Applications; Mathematics, Applied; Statistics & Probability; CPCI-S(ISTP); 6
语种	英语
出处	SCI
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/406921]
专题	数学科学学院
推荐引用方式 GB/T 7714	Hickernell, FJ,Sloan, IH,Wasilkowski, GW. The strong tractability of multivariate integration using lattice rules. 2004-01-01.

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