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Combinatorial Methods for Matrix Computation in Dynamical Systems Analysis

Research Project

Project/Area Number 25730009
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Mathematical informatics
Research InstitutionChuo University

Principal Investigator

TAKAMATSU Mizuyo  中央大学, 理工学部, 准教授 (70580059)

Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords行列束 / 微分代数方程式 / Kronecker標準形 / 混合行列理論 / 動的システム解析 / 指数 / 組合せ緩和 / 可制御性 / 電気回路
Outline of Final Research Achievements

Many modeling and simulation tools for dynamical systems adopt algorithms based on the structural approach. An advantage of the structural approach is that it is supported by efficient combinatorial algorithms that are free from errors in numerical computation. On the other hand, however, algorithms based on the structural approach sometimes fail because they discard numerical information.
Combinatorial matrix theory is a branch of mathematics that combines combinatorial optimization techniques and matrix computation. In this research, we develop algorithms to analyze dynamical systems based on combinatorial matrix theory.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (9 results)

All 2017 2016 2015 2014 2013

All Journal Article (3 results) (of which Peer Reviewed: 3 results,  Acknowledgement Compliant: 1 results) Presentation (6 results) (of which Int'l Joint Research: 1 results)

  • [Journal Article] On the Kronecker canonical form of singular mixed matrix pencils2017

    • Author(s)
      S. Iwata and M. Takamatsu
    • Journal Title

      SIAM Journal on Control and Optimization

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Matching problems with delta-matroid constraints2014

    • Author(s)
      Naonori Kakimura and Mizuyo Takamatsu
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: 28 Issue: 2 Pages: 942-961

    • DOI

      10.1137/110860070

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Structural characterization of hybrid equations with tractability index at most two2014

    • Author(s)
      Mizuyo Takamatsu
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 411 Issue: 2 Pages: 639-651

    • DOI

      10.1016/j.jmaa.2013.10.018

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Index Reduction via Unimodular Transformations2017

    • Author(s)
      S. Iwata and M. Takamatsu
    • Organizer
      The 10th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
    • Place of Presentation
      Budapest
    • Year and Date
      2017-05-22
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 混合行列束のKronecker標準形に関する組合せ論的解析とシステム制御への応用2016

    • Author(s)
      高松瑞代
    • Organizer
      日本オペレーションズ・リサーチ学会「最適化の基盤とフロンティア」研究部会第6回研究会
    • Place of Presentation
      横浜
    • Year and Date
      2016-03-19
    • Related Report
      2015 Research-status Report
  • [Presentation] 構造可制御部分空間のマトロイド理論的解析2016

    • Author(s)
      岩田覚, 高松瑞代
    • Organizer
      日本応用数理学会2016年研究部会連合発表会
    • Place of Presentation
      神戸
    • Year and Date
      2016-03-05
    • Related Report
      2015 Research-status Report
  • [Presentation] ユニモジュラ変換による微分代数方程式の指数減少法2016

    • Author(s)
      岩田覚, 高松瑞代
    • Organizer
      日本応用数理学会2016年度年会
    • Place of Presentation
      北九州
    • Related Report
      2016 Annual Research Report
  • [Presentation] 非正則混合行列束のKronecker標準形に関する組合せ論的解析2015

    • Author(s)
      岩田覚, 高松瑞代
    • Organizer
      日本応用数理学会2015年度年会
    • Place of Presentation
      金沢
    • Year and Date
      2015-09-09
    • Related Report
      2015 Research-status Report
  • [Presentation] On the Kronecker canonical form of singular mixed matrix pencils2013

    • Author(s)
      Satoru Iwata and Mizuyo Takamatsu
    • Organizer
      The 8th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications
    • Place of Presentation
      Veszprem
    • Related Report
      2013 Research-status Report

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

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