2011 Fiscal Year Final Research Report
Project/Area Number |
21654004
|
Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
Allocation Type | Single-year Grants |
Research Field |
Algebra
|
Research Institution | Hiroshima University |
Principal Investigator |
SAITO Mutsuo 広島大学, 大学院・理学研究科, 助教 (30507736)
|
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)
|
Project Period (FY) |
2009 – 2011
|
Keywords | 数論 / 超一様分布列 / 超一様点集合 |
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.
|
Research Products
(7 results)