| Project/Area Number |
21654004
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Hiroshima University |
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Principal Investigator |
SAITO Mutsuo 広島大学, 大学院・理学研究科, 助教 (30507736)
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| Co-Investigator(Renkei-kenkyūsha) |
MATSUMOTO Makoto 東京大学, 数理科学研究科, 教授 (70231602)
NISHIMURA Takuji 山形大学, 理学部, 准教授 (90333947)
HARAMOTO Hiroshi 愛媛大学, 教育学研究科, 講師 (40511324)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,440,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2009: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | 数論 / 超一様分布列 / 超一様点集合 / 均等分布 / GPGPU / Walsh関数 / 均等分布次元 |
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| Research Abstract |
We have developed a new figure of merit of Low Discrepancy Sequence(LDS), called Walsh Figure Of Merit(WAFOM). WFOM is a function that takes point set in a unit hypercube in S-dimensional space and gives a real number as figure of merit of the point set. WAFOM can be used to evaluate the upper bound of the error of numerical integration. We gave a proof that the order of calculation of WAFOM is O(nSN) by using discrete Fourier inverse transformation, where n is number of bits below radix point of binary form, S is number of dimension and N is number of points in the LDS. WAFOM makes finding new LDS easy because of faster calculation speed compared to existing method to calculate figure of merit of LDS.
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