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Application of uniformity and hyper uniformity in sciences

Research Project

Project/Area Number 26310211
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section特設分野
Research Field Mathematical Sciences in Search of New Cooperation
Research InstitutionHiroshima University

Principal Investigator

Matsumoto Makoto  広島大学, 理学研究科, 教授 (70231602)

Project Period (FY) 2014-07-18 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥14,040,000 (Direct Cost: ¥10,800,000、Indirect Cost: ¥3,240,000)
Fiscal Year 2018: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2017: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2015: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2014: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Keywords準モンテカルロ法 / 超一様性 / WAFOM / difference set / design / quasi-Monte Carlo / 疑似乱数 / 一様性 / 擬似乱数
Outline of Final Research Achievements

Monte Carlo integration of a function f on a hypercube means to generate uniformly random sample points on the hypercube, and then take the average of the function evaluated at these points as a numerical approximation of the integration of f. Quasi-Monte Carlo integration is to choose hyper-uniform sample points to make the integration error smaller. Widely known point sets uses the t-value as a figure of merit. In this study we introduced "WAFOM with parameters" as a new figure of merit, and obtained hyper-uniform point sets according to this index. It is experimentally shown that the new point sets perform better than existing methods, for relatively smooth integrands

Academic Significance and Societal Importance of the Research Achievements

モンテカルロ積分・準モンテカルロ積分は、高い次元の空間上の積分を行う際に有用であり、工学・科学・金融など幅広い応用を持つ。モンテカルロ積分法では、次元に無関係に誤差をサンプルポイント数の-0.5乗で小さくできるが、この誤差収束の遅さが問題となることも多い。本研究では、滑らかな関数に対しては誤差収束をNの-1乗以上に効率化する点集合の構成法を与えた。また、滑らかでない関数に対しても従来広く使われているlow discrepancy点集合と同程度の性能を持つことを実験的に示した。

Report

(7 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • Research Products

    (19 results)

All 2019 2018 2017 2016 2015 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results,  Acknowledgement Compliant: 2 results) Presentation (11 results) (of which Int'l Joint Research: 5 results,  Invited: 1 results) Remarks (2 results)

  • [Journal Article] Approximation of Quasi-Monte Carlo worst case error in weighted spaces of infinitely times smooth functions2018

    • Author(s)
      Matsumoto Makoto、Ohori Ryuichi、Yoshiki Takehito
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 330 Pages: 155-164

    • DOI

      10.1016/j.cam.2017.08.010

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Method to Compute an Appropriate Sample Size of the Two-Level Test for NIST Test Suite2018

    • Author(s)
      Hiroshi Haramoto, Makoto Matsumoto
    • Journal Title

      Monte Carlo and Quasi-Monte Carlo Methods 2016

      Volume: 印刷中

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Characterization of matrices B such that (I , B , B^2) generates a digital net with t -value zero2018

    • Author(s)
      Kajiura Hiroki、Matsumoto Makoto、Suzuki Kosuke
    • Journal Title

      Finite Fields and Their Applications

      Volume: 52 Pages: 289-300

    • DOI

      10.1016/j.ffa.2018.04.011

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Walsh Figure of Merit for Digital Nets: An Easy Measure for Higher Order Convergent QMC2016

    • Author(s)
      Makoto Matsumoto, Ryuichi Ohori
    • Journal Title

      the series Springer Proceedings in Mathematics & Statistics

      Volume: 163 Pages: 143-160

    • DOI

      10.1007/978-3-319-33507-0_5

    • ISBN
      9783319335056, 9783319335070
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A search for extensible low-WAFOM point sets2016

    • Author(s)
      Shin Harase
    • Journal Title

      Monte Carlo Methods and Applications

      Volume: 22 Issue: 4 Pages: 349-357

    • DOI

      10.1515/mcma-2016-0119

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Quasi-Monte Carlo point sets with small t-values and WAFOM2015

    • Author(s)
      Shin Harase
    • Journal Title

      Applied Mathematics and Computation

      Volume: 254 Pages: 318-326

    • DOI

      10.1016/j.amc.2014.12.144

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Presentation] A visible aw of xorshift128+ generators2019

    • Author(s)
      Haramoto Hiroshi
    • Organizer
      MCM2019
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Checking the Soundness of Statistical Tests for Random Number Generators by Using a Three-Level Test2017

    • Author(s)
      Hiroshi Haramoto
    • Organizer
      International Conference on Monte Carlo Methods and its Applications 2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Method to Compute an Appropriate Sample Size of the Two-Level Test of NIST Test Suite for Frequency and Binary Matrix Rank Test2016

    • Author(s)
      Hiroshi Haramoto, Makoto Matsumoto
    • Organizer
      12th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, MCQMC 2016
    • Place of Presentation
      Stanford University, USA
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] NISTの二重検定における適切なサンプル数の決定2016

    • Author(s)
      原本博史, 松本眞
    • Organizer
      日本応用数理学会2016年度年会
    • Place of Presentation
      北九州国際会議場
    • Related Report
      2016 Annual Research Report
  • [Presentation] Sobol'列と計算ファイナンスへの応用2016

    • Author(s)
      原瀬 晋,湯浅智意
    • Organizer
      乱数と超一様性集会
    • Place of Presentation
      東京大学(本郷キャンパス)
    • Related Report
      2016 Annual Research Report
  • [Presentation] A comparison study of Sobol' sequences in financial derivatives2016

    • Author(s)
      Shin Harase, Tomooki Yuasa
    • Organizer
      12th International Conference on Monte Carlo and Quasi-Monte Carlo
    • Place of Presentation
      Stanford University, USA
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] メルセンヌツイスタ擬似乱数発生法の連結について2016

    • Author(s)
      原瀬 晋
    • Organizer
      日本応用数理学会2016年度年会
    • Place of Presentation
      北九州国際会議場
    • Related Report
      2016 Annual Research Report
  • [Presentation] メルセンヌツイスタ擬似乱数発生法の連結について2016

    • Author(s)
      原瀬 晋
    • Organizer
      2016年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学
    • Related Report
      2016 Annual Research Report
  • [Presentation] ``WAFOM with parameter for higher QMC: Revenge of the algebraic code, Part II''2015

    • Author(s)
      Makoto Matsumoto
    • Organizer
      10th IMACS Seminar on Monte Carlo Methods, JKU, Linz, Austria.
    • Place of Presentation
      Linz, Austria.
    • Year and Date
      2015-07-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 準モンテカルロ法超入門(Walsh Figure of Meritからの)2015

    • Author(s)
      松本眞
    • Organizer
      愛媛代数学セミナー
    • Place of Presentation
      愛媛大学
    • Year and Date
      2015-04-20
    • Related Report
      2015 Annual Research Report
  • [Presentation] 準モンテカルロ法・超入門(Walsh figure of meritからの)2015

    • Author(s)
      松本 眞
    • Organizer
      愛媛代数学セミナー
    • Place of Presentation
      愛媛大学
    • Year and Date
      2015-04-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Remarks] Rによる準モンテカルロ積分法

    • URL

      https://mersennetwister-lab.github.io/rmcqmcint/index-ja.html

    • Related Report
      2017 Annual Research Report
  • [Remarks] C++によるモンテカルロ・準モンテカルロ積分法

    • URL

      https://mersennetwister-lab.github.io/MCQMCIntegration/ja/index.html

    • Related Report
      2017 Annual Research Report

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Published: 2014-09-09   Modified: 2023-03-23  

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