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Constructing cubature formula and its application to design of experiments

Research Project

Project/Area Number 25870756
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Foundations of mathematics/Applied mathematics
Algebra
Research InstitutionAichi Prefectural University (2014-2015)
Tokyo Woman's Christian University (2013)

Principal Investigator

HIRAO Masatake  愛知県立大学, 情報科学部, 准教授 (90624073)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordscubature公式 / 最適計画 / 回転可能計画 / 球面上のデザイン / ユークリッド空間上のデザイン / 作用素型cubature公式 / Cubature公式 / QMCデザイン / 確率点過程 / Laplace作用素型cubature公式
Outline of Final Research Achievements

We consider a novel type of cubature formulas called operator-type cubature formulas. We give a lower bound for the number of points needed, and discuss analytic conditions for equality, together with tight illustrations for Laplacian-type cubature.
On the other hand, we also consider constructing classical cubature problems of higher degree cases. We provides a systematic treatment of a group-theoretic approach for constructing classical cubature formulas and designs. Moreover, we give a method of reconstruction of formulas via combinatorial designs.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (20 results)

All 2016 2015 2014 2013 Other

All Int'l Joint Research (1 results) Journal Article (3 results) (of which Peer Reviewed: 2 results,  Acknowledgement Compliant: 1 results,  Open Access: 1 results) Presentation (14 results) (of which Int'l Joint Research: 1 results) Remarks (2 results)

  • [Int'l Joint Research] University of New South Wales(Australia)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Some remarks on cubature formulas with linear operators2015

    • Author(s)
      Masatake Hirao, Takayuki Okuda, Masanori Sawa
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 印刷中

    • NAID

      130006887144

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Constructions of Φp-optimal rotational designs on the ball2015

    • Author(s)
      M. Hirao, M. Sawa and M. Jimbo
    • Journal Title

      Sankhya -- The Indian Journal of Statistics

      Volume: 77 Issue: 1 Pages: 211-236

    • DOI

      10.1007/s13171-014-0053-4

    • Related Report
      2013 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] 最適計画の構成法とその関連した話題2013

    • Author(s)
      平尾将剛,澤正憲,神保雅一
    • Journal Title

      数理解析研究所講究録

      Volume: 1844 Pages: 23-38

    • Related Report
      2013 Research-status Report
  • [Presentation] 超八面体の辺の等分点を用いたD最適実験計画の構成法について2016

    • Author(s)
      澤正憲,平尾将剛,山本裕貴
    • Organizer
      日本数学会2016度年会
    • Place of Presentation
      筑波大学(茨城県・つくば市)
    • Year and Date
      2016-03-18
    • Related Report
      2015 Annual Research Report
  • [Presentation] 行列式点過程を用いた 球面上の準モンテカルロデザイン系列の生成について2015

    • Author(s)
      平尾将剛
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学瀬田キャンパス(滋賀県・大津市)
    • Year and Date
      2015-12-19
    • Related Report
      2015 Annual Research Report
  • [Presentation] QMC design sequences generated by determinantal point processes on the sphere2015

    • Author(s)
      平尾将剛
    • Organizer
      日本数学会2015年度秋期総合分科会
    • Place of Presentation
      京都産業大学(京都府・京都市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] Spherical designs and determinantal point processes2015

    • Author(s)
      平尾将剛
    • Organizer
      Workshop on Spherical Design and Numerical Analysis
    • Place of Presentation
      上海交通大学,上海(中国)
    • Year and Date
      2015-04-22
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 球面上の実験計画法への行列式点過程アプローチ2015

    • Author(s)
      平尾将剛
    • Organizer
      研究集会「有限幾何と組合せデザイン」
    • Place of Presentation
      東京理科大学
    • Year and Date
      2015-03-07
    • Related Report
      2014 Research-status Report
  • [Presentation] 行列式点過程を用いた球面上の実験計画法の構築に向けて2015

    • Author(s)
      平尾将剛
    • Organizer
      熊本組合せ論研究集会「代数的デザイン論とその周辺」
    • Place of Presentation
      熊本大学
    • Year and Date
      2015-01-09
    • Related Report
      2014 Research-status Report
  • [Presentation] Characterizing optimum designs in terms of finite irreducible refection groups2014

    • Author(s)
      平尾将剛,神保雅一,澤正憲
    • Organizer
      Algebraic Combinatorics Workshop
    • Place of Presentation
      University of Science and Technology of China
    • Year and Date
      2014-11-28
    • Related Report
      2014 Research-status Report
  • [Presentation] Characterizing optimum designs in terms of finite irreducible refection groups. II2014

    • Author(s)
      平尾将剛,澤正憲
    • Organizer
      2014年度数学会秋期総合分科会
    • Place of Presentation
      広島大学
    • Year and Date
      2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] Some remarks on operator-type cubature formulas2014

    • Author(s)
      平尾将剛,奥田隆幸,澤正憲
    • Organizer
      The Japanese Conference on Combinatorics and its Applications
    • Place of Presentation
      文部科学省研究交流センター
    • Year and Date
      2014-08-26
    • Related Report
      2014 Research-status Report
  • [Presentation] A construction of optimum designs on the ball using the orbits of finite irreducible refection groups2014

    • Author(s)
      平尾将剛,澤正憲
    • Organizer
      Japan Conference on Graph Theory and Combinatorics 2014
    • Place of Presentation
      日本大学
    • Year and Date
      2014-05-20
    • Related Report
      2014 Research-status Report
  • [Presentation] 球面上の統計的実験計画法と立体求積公式

    • Author(s)
      平尾将剛,澤正憲
    • Organizer
      日本応用数理学会2013年度年会
    • Place of Presentation
      福岡(アクロス福岡)
    • Related Report
      2013 Research-status Report
  • [Presentation] n 次元球上の最適計画の構成について

    • Author(s)
      平尾将剛,澤正憲,神保雅一
    • Organizer
      日本数学会2013年度秋季総合分科会
    • Place of Presentation
      愛媛(愛媛大学)
    • Related Report
      2013 Research-status Report
  • [Presentation] Characterizing optimum designs in terms of finite irreducible reflection groups

    • Author(s)
      平尾将剛,澤正憲
    • Organizer
      第10回「代数学と計算」
    • Place of Presentation
      東京(首都大学東京)
    • Related Report
      2013 Research-status Report
  • [Presentation] Characterizing optimum designs in terms of finite irreducible reflection groups

    • Author(s)
      平尾将剛,澤正憲
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京(学習院大学)
    • Related Report
      2013 Research-status Report
  • [Remarks] Masatake Hirao's Home page

    • URL

      http://www.ist.aichi-pu.ac.jp/~hirao/

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
  • [Remarks] Masatake Hirao's Home page

    • URL

      http://lab.twcu.ac.jp/hirao/

    • Related Report
      2013 Research-status Report

URL: 

Published: 2014-07-25   Modified: 2019-07-29  

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