Approximation of Quasi-Monte Carlo worst case error in weighted spaces of infinitely times smooth functions
Approximation of Quasi-Monte Carlo worst case error in weighted spaces of infinitely times smooth functions
复制标题
无限次平滑函数加权空间中拟蒙特卡罗最坏情况误差的逼近
DOI：
10.1016/j.cam.2017.08.010
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发表时间：
2018
影响因子：
2.4
通讯作者：
Yoshiki Takehito
中科院分区：
文献类型：
--
作者：
Matsumoto Makoto;Ohori Ryuichi;Yoshiki Takehito
本文利用F2上的数字网研究了C∞[0，1] s中加权光滑函数类的拟蒙特卡罗（QMC）最坏情况误差.我们表明，指数函数的QMC积分误差的最坏情况下的错误的比率是有界的常数上下。这一结果为我们提供了一个简单的解释，即对于指数函数具有小QMC积分误差的数字网络也给出了该函数空间中任何函数的小积分误差。
In this paper, we consider Quasi-Monte Carlo (QMC) worst case error of weighted smooth function classes in C∞[0, 1] s by a digital net over F 2. We show that the ratio of the worst case error to the QMC integration error of an exponential function is bounded above and below by constants. This result provides us with a simple interpretation that a digital net with small QMC integration error for an exponential function also gives the small integration error for any function in this function space.