Constructing a new class of low-discrepancy sequences by using the β-adic transformation
Constructing a new class of low-discrepancy sequences by using the β-adic transformation
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使用 β-adic 变换构造一类新的低差异序列
DOI：
10.1016/s0378-4754(98)00115-3
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
Syoiti Ninomiya
中科院分区：
文献类型：
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作者：
Syoiti Ninomiya
众所周知，低差异序列及其差异在拟蒙特卡罗方法中起着至关重要的作用[5]。本文利用遍历理论变换β-adic变换[7，8]构造了一类新的低偏差序列Nβ。这里，β是大于1的真实的数。当β为大于2的整数时，Nβ成为以β为基的经典货车derCorput序列.因此，类Nβ可以看作是货车derCorput序列的推广.结果表明，对于某些特殊的β，这个序列的差异以最快的顺序O（N-1 log N）减少。我们给出了某些βs的Nβ偏差的数值结果。Pagès [6]还利用遍历变换在不同方向上推广了货车的Corput序列。
It is well known that low-discrepancy sequences and their discrepancy play essential roles in quasi Monte Carlo methods [5]. In this paper, a new class of low-discrepancy sequences Nβis constructed by using the ergodic theoretical transformation which is called β-adic transformation [7, 8]. Here, β is a real number greater than 1. When β is an integer greater than 2, Nβbecomes the classical van der Corput sequence in base β. Therefore, the class Nβcan be regarded as a generalization of the van der Corput sequence. It is shown that for some special β, the discrepancy of this sequence decreases in the fastest order O (N−1log N) . We give the numerical results of discrepancy of Nβfor some βs. Pagès [6] also generalized van der Corput sequence in a different direction by using an ergodic transformation.