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Higher order hyper uniform point sets and higher order quasi-Monte Carlo method

Research Project

Project/Area Number 15K13460
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionHiroshima University

Principal Investigator

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

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)
Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords準モンテカルロ法 / 数値積分 / WAFOM / 擬似乱数 / 超一様点集合 / 疑似乱数
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.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (19 results)

All 2018 2017 2016 2015 Other

All Int'l Joint Research (1 results) Journal Article (6 results) (of which Peer Reviewed: 6 results,  Acknowledgement Compliant: 2 results) Presentation (10 results) (of which Int'l Joint Research: 6 results) Remarks (2 results)

  • [Int'l Joint Research] University of New South Wales/Fuculty of Science(オーストラリア)

    • Related Report
      2015 Research-status Report
  • [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 Research-status 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 Research-status 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 Research-status Report
    • Peer Reviewed
  • [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 Research-status 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 Research-status 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 Research-status 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 Methods in Scientific Computing (MCQMC 2016)
    • Place of Presentation
      Stanford University, USA
    • Related Report
      2016 Research-status 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 Research-status 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 Research-status Report
  • [Presentation] WAFOM with parameter for higher QMC: Revenge of the algebraic code, Part II2015

    • 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 Research-status Report
    • Int'l Joint Research
  • [Presentation] A fast QMC computation by low-WAFOM point sets for cumulative distribution of multivariate normal distributions2015

    • Author(s)
      Shinsuke Mori, Ryuichi Ohori, Hiroki Kajiura, 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 Research-status Report
    • Int'l Joint Research
  • [Presentation] A method to check soundness of statistical tests on randomness2015

    • Author(s)
      Hiroshi Haramoto
    • 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 Research-status Report
    • Int'l Joint Research
  • [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: 2015-04-16   Modified: 2019-03-29  

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