New figure of merits for quasi-Monte Carlo point set

2015 Fiscal Year Final Research Report

• Project/Area Number: 24654019
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Hiroshima University (2013-2015); The University of Tokyo (2012)
• Principal Investigator: Matsumoto Makoto 広島大学, 理学(系)研究科(研究院), 教授 (70231602)
• Co-Investigator(Renkei-kenkyūsha): Nishimura Takuji 山形大学, 理学部, 准教授 (90333947) ; Hagita Mariko お茶の水女子大学, 大学院人間文化創成科学研究科, 准教授 (70338218) ; Haramoto Hiroshi 愛媛大学, 教育学部, 講師 (40511324)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 準モンテカルロ法 / 数値積分

Outline of Final Research Achievements

Numerical integration over a high dimensional space appears in many area in sciences. A major algorithm is Monte Carlo method, but the order of the estimated error, inverse of square root of N, where N is the size of point sets, is relatively large. Quasi-Monte Carlo method is to choose a "good" point set to make the error much smaller. In this research, as a criterion on the hyper uniformity of point sets, Walsh figure of merit is introduced. It directly bounds the integration error, and it is efficiently computable. More over, we introduced "derivation sensitivity parameter", which makes the point set effective for higher dimensions. The point set is available from a homepage. We conducted several numerical experiments, which show advantages of the proposed point sets over existing ones.

Free Research Field

擬似乱数、準モンテカルロ法