2017 Fiscal Year Final Research Report
Higher order hyper uniform point sets and higher order quasi-Monte Carlo method
| Project/Area Number |
15K13460
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Hiroshima University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
HAGITA Mariko お茶の水女子大学, 大学院人間文化創成科学研究科, 教授 (70338218)
NISHIMURA Takuji 山形大学, 理学部, 准教授 (90333947)
HARAMOTO Hiroshi 愛媛大学, 教育学部, 講師 (40511324)
HARASE Shin 立命館大学, 理工学部, 数学嘱託講師 (80610576)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 準モンテカルロ法 / 数値積分 / WAFOM / 擬似乱数 |
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| Outline of Final Research Achievements |
Let f be an integrand function defined on an s-dimensional hyper cube. Quasi-Monte Carlo method is to choose a point set P of size N in this hyper cube, and obtain numerical approximation of the integral of f by the mean value of f over P. When P is chosen uniformly randomly, the integration error is known to converge with order N's power to -1/2. Classical Quasi-Monte Carlo tries to design a good P with order nearly 1/N. Our research focuses on an index called parameterized Walsh Figure of Merit. By searching for P with small value of this index, we find P with smaller error than previously proposed point sets. In particular, for low dimensions s<5, our method shows remarkable improvements.
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| Free Research Field |
代数学
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