Low Discrepancy Sequence

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

• [Journal Article] Fast lattice reduction forF2-linear pseudorandom numbergenerator (2011)
  • Author(s): Shin Harase, Makoto Matsumoto, MutsuoSaito
  • Journal Title: Mathematics of Computation Volume: vol.80 Pages: 395-407
  • Peer Reviewed
• [Presentation] A deviation ofCURAND : standard pseudorandom numbergenerator in CUDA for GPGPU (2012)
  • Author(s): Makoto Matsumoto
  • Organizer: Tenth International Conference on MonteCarlo and Quasi-Monte Carlo Methods inScientific Computing
  • Place of Presentation: Sydney, Australia
  • Year and Date: 2012-02-13
• [Presentation] Variants of Mersennetwister suitable for graphicprocessors (2010)
  • Author(s): Makoto Matsumoto
  • Organizer: 9th InternationalConference on Monte Carlo andQuasi-Monte Carlo Methods inScientific Computing
  • Place of Presentation: Warsaw, Poland
  • Year and Date: 2010-08-15
• [Remarks]
  • URL: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MTGP
• [Remarks]
  • URL: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/TINYMT
• [Remarks]
  • URL: http://arxiv.org/abs/1109.3873
• [Remarks]
  • URL: http://arxiv.org/abs/1005.4973