Quasi-Monte Carlo methods can be efficient for integration over products of spheres
نویسندگان
چکیده
منابع مشابه
Quasi-Monte Carlo methods can be efficient for integration over products of spheres
We study the worst-case error of quasi-Monte Carlo rules for multivariate integration in some weighted Sobolev spaces of functions defined on the product of d copies of the unit sphere Ss ⊆ Rs+1. The space is a tensor product of d reproducing kernel Hilbert spaces defined in terms of uniformly bounded ‘weight’ parameters γd,a for a = 1, 2, . . . , d. We prove that strong QMC tractability holds ...
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Quasi-Monte Carlo (QMC) methods for high dimensional integrals have been well studied for the unit cube. Sloan and Woźniakowski [18] partially solve the question of why they are significantly more efficient than Monte carlo methods. Kuo and Sloan [9] prove similar results for integration over product of spheres. We study the QMC tractability of integrals of functions defined over the product of...
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ژورنال
عنوان ژورنال: Journal of Complexity
سال: 2005
ISSN: 0885-064X
DOI: 10.1016/j.jco.2004.07.001