期刊论文

Projection weighted symmetric discrepancy

中文

中国科学：数学

1674-7216

2020

50

5

629-644

10.1360/N012019-00014

国家自然科学基金(批准号:11571133和11871237)资助项目。

本校为第一机构

均匀设计自20世纪80年代被提出以来依靠其稳健和使用方便、灵活的特性而广受欢迎.为获得实验目标区域内散布均匀的设计点集,不同的均匀度量标准被相继提出,其中以从数值积分理论中发展而来的L2-星偏差及相应的改进形式接受度最为广泛.尽管相对于最初的星偏差标准,当前广泛使用的改进偏差有更好的性质和实用性,但这些偏差仍存在一些缺点,例如,中心化偏差（centered discrepancy, CD）对于实验目标区域中心点的特殊依赖性.从各种偏差定义的本源上可以看出,对称偏差（symmetric discrepancy, SD）相较于CD有更好的几何性质, SD给实验目标区域内任何点的权重都是相同的,这在直观上更符合均匀性的要求...

The uniform design was proposed in the 1980s, and since then lots of researchers have studied it. In order to distribute the points evenly in the experimental domain, many criteria have been forwarded to measure the uniformity of the design array. Among those criteria, the L2-discrepancies, developed from star discrepancy in the number theoretic method, are the most popular measurement, such as the centered L2-discrepancy(CD). There are still some disadvantages with those discrepancies. For example, the central points of the experimental domain plays a much more important role than other point...