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【期刊论文】Computational complexity of the integration problem for anisotropic classes
叶培新, Ye Peixin
Advances in Computational Mathematics (2005) 23: 375–392 ,-0001,():
-1年11月30日
We determine the exact order of ε-complexity of the numerical integration problem for the anisotropic class Wr∞ (I d ) and Hr∞ (I d ) with respect to the worst case randomized methods and the average case deterministic methods. We prove this result by developing a decomposition technique of Borel measure on unit cube of d-dimensional Euclidean space. Moreover by the imbedding relationship between function classes we extend our results to the classes of functions W^ p (I d ) and H^ p (I d ). By the way we highlight some typical results and stress the importance of some open problems related to the complexity of numerical integration.
ntegration problem, ε-complexity, randomized methods, anisotropic classes
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