Monte Carlo methods for uniform approximation on periodic Sobolev spaces with mixed smoothness
Monte Carlo methods for uniform approximation on periodic Sobolev spaces with mixed smoothness
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DOI：
10.1016/j.jco.2017.12.002
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发表时间：
2017-09
期刊：
影响因子：
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通讯作者：
G. Byrenheid;R. Kunsch;V. K. Nguyen
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文献类型：
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作者：
G. Byrenheid;R. Kunsch;V. K. Nguyen
通过使用任意线性信息的方法，我们考虑了定义在环面Td上的具有占优混合光滑性的具有1<；p<；∞的紧嵌入到L∞(Td)空间的线性和非线性蒙特卡罗逼近的收敛阶.这些情况很有趣，因为与确定性近似相比，我们可以在主速率上获得高达1/2的加速比。在此过程中，我们确定了方和段(2007、2008)悬而未决的一些案件的比率。
We consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness with integrability 1< p<∞ defined on the torus T d into the space L∞(T d) via methods that use arbitrary linear information. These cases are interesting because we can gain a speedup of up to 1∕ 2 in the main rate compared to deterministic approximation. In doing so we determine the rate for some cases that have been left open by Fang and Duan (2007, 2008).