Sobol序列
蒙特卡罗方法
拟蒙特卡罗方法
序列(生物学)
采用蒙地卡罗积分法
数值积分
应用数学
数学
算法
计算机科学
混合蒙特卡罗
统计
马尔科夫蒙特卡洛
数学分析
生物
遗传学
作者
Ladislav Kocis,W. J. Whiten
出处
期刊:ACM Transactions on Mathematical Software
[Association for Computing Machinery]
日期:1997-06-01
卷期号:23 (2): 266-294
被引量:326
标识
DOI:10.1145/264029.264064
摘要
The Halton, Sobol, and Faure sequences and the Braaten-Weller construction of the generalized Halton sequence are studied in order to assess their applicability for the quasi Monte Carlo integration with large number of variates. A modification of the Halton sequence (the Halton sequence leaped) and a new construction of the generalized Halton sequence are suggested for unrestricted number of dimensions and are shown to improve considerably on the original Halton sequence. Problems associated with estimation of the error in quasi Monte Carlo integration and with the selection of test functions are identified. Then an estimate of the maximum error of the quasi Monte Carlo integration of nine test functions is computed for up to 400 dimensions and is used to evaluate the known generators mentioned above and the two new generators. An empirical formula for the error of the quasi Monte Carlo integration is suggested.
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