Combinatorial Optimization Approach to Optimal Differential-Algebraic Equations Modeling

• Project/Area Number: 22860057
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Engineering fundamentals
• Research Institution: Chuo University
• Principal Investigator: TAKAMATSU Mizuyo 中央大学, 理工学部, 助教 (70580059)
• Project Period (FY): 2010 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥3,146,000 (Direct Cost: ¥2,420,000、Indirect Cost: ¥726,000); Fiscal Year 2011: ¥1,508,000 (Direct Cost: ¥1,160,000、Indirect Cost: ¥348,000); Fiscal Year 2010: ¥1,638,000 (Direct Cost: ¥1,260,000、Indirect Cost: ¥378,000)
• Keywords: 微分代数方程式 / 混合解析 / 行列束 / 組合せ最適化 / 数値計算 / 混合行列理論 / 指数 / 回路シミュレーション / 組合せ的行列理論 / 組合せ緩和 / クロネッカー標準形

Research Abstract

Dynamical systems which appear in numerical simulation are often described by differential-algebraic equations(DAEs). In order to improve accuracy of numerical simulation, a great deal of research has been made on numerical solution methods. However, accuracy depends not only on how to solve but also on what to solve. This research has developed methods to obtain DAEs which are easy to solve numerically.

Research Products

• [Journal Article] Computing the maximum degree of minors in mixed polynomial matrices via combinatorial relaxation (2012)
  • Author(s): S.Iwata, M.Takamatsu
  • Journal Title: Algorithmica Volume: (掲載決定)(印刷中) Issue: 2 Pages: 346-368
  • DOI: 10.1007/s00453-012-9640-8
  • Year and Date: 2012-03-16
  • Peer Reviewed
• [Journal Article] Tractability index of hybrid equations for circuit simulation (2012)
  • Author(s): S. Iwata, M. Takamatsu, and S. Iwata, M. Takamatsu, and C. Tischendorf
  • Journal Title: Mathematics of Computation Volume: vol.81 Pages: 923-939
  • Peer Reviewed
• [Journal Article] Tractability index of hybrid equations for circuit simulation (2012)
  • Author(s): S.Iwata, M.Takamatsu, C.Tischendorf
  • Journal Title: Mathematics of Computation Volume: 81 Issue: 278 Pages: 923-939
  • DOI: 10.1090/s0025-5718-2011-02558-5
  • Peer Reviewed
• [Journal Article] On the Kronecker canonical form of mixed matrix pencils (2011)
  • Author(s): S. Iwata and M. Takamatsu
  • Journal Title: SIAM Journal on Matrix Analysis and Applications Volume: vol.32 Pages: 44-71
  • Peer Reviewed
• [Journal Article] On the Kronecker canonical form of mixed matrix pencils (2011)
  • Author(s): S.Iwata, M.Takamatsu
  • Journal Title: SIAM Journal on Matrix Analysis and Applications Volume: 32 Pages: 44-71
  • Peer Reviewed
• [Journal Article] Hybrid analysis of nonlinear time-varying circuits providing DAEs with index at most one (2010)
  • Author(s): S. Iwata, M. Takamatsu, and C. Tischendorf
  • Journal Title: Scientific Computing in Electrical Engineering SCEE 2008(J. Roos and L. R. J. Costa eds.) Pages: 151-158
  • Peer Reviewed
• [Journal Article] Index characterization of differential-algebraic equations in hybrid analysis for circuit simulation (2010)
  • Author(s): M. Takamatsu and S. Iwata
  • Journal Title: International Journal of Circuit Theory and Applications Volume: vol.38 Pages: 419-440
  • Peer Reviewed
• [Journal Article] 非線形時変回路に対する混合方程式の組合せ論的解析-グラフ構造による順良指数の特徴付け- (2010)
  • Author(s): 岩田覚, 高松瑞代, Caren Tischendorf
  • Journal Title: 数理解析研究所講究録「21世紀の数理計画:アルゴリズムとモデリング」 Volume: 1676 Pages: 36-50
• [Journal Article] Index characterization of differential-algebraic equations in hybrid analysis for circuit simulation (2010)
  • Author(s): M.Takamatsu, S.Iwata
  • Journal Title: International Journal of Circuit Theory and Applications Volume: 38 Pages: 419-440
• [Journal Article] Hybrid analysis of nonlinear time-varying circuits providing DAEs with index at most one (2010)
  • Author(s): S.Iwata, M.Takamatsu, C.Tischendorf
  • Journal Title: Scientific Computing in Electrical Engineering SCEE 2008 Pages: 151-158
  • Peer Reviewed
• [Journal Article] Computing the maximum degree of minors in mixed polynomial matrices via combinatorial relaxation
  • Author(s): S. Iwata and M. Takamatsu
  • Journal Title: Algorithmica Volume: (to appear)
  • Peer Reviewed
• [Presentation] 指数2の混合方程式を導く回路の構造的特徴付け (2012)
  • Author(s): 高松瑞代
  • Organizer: 日本応用数理学会2012年研究部会連合発表会
  • Place of Presentation: 福岡
  • Year and Date: 2012-03-08
• [Presentation] 指数2の混合方程式を導く回路の構造的特徴付け (2012)
  • Author(s): 高松瑞代
  • Organizer: 日本応用数理学会2012年研究部会連合発表会
  • Place of Presentation: 九州大学伊都キャンパス
  • Year and Date: 2012-03-08
• [Presentation] Computing the maximum degree of minors in mixed polynomial matrices via combinatorial relaxation (2011)
  • Author(s): S. Iwata and M. Takamatsu
  • Organizer: The 15th Conference on Integer Programming and Combinatorial Optimization(IPCO XV)
  • Place of Presentation: New York
  • Year and Date: 2011-06-16
• [Presentation] Computing the maximum degree of minors in mixed polynomial matrices via combinatorial relaxation (2011)
  • Author(s): S.Iwata, M.Takamatsu
  • Organizer: The 15th Conference on Integer Programming and Combinatorial Optimization (IPCO XV)
  • Place of Presentation: IBM Learning Center
  • Year and Date: 2011-06-16
• [Presentation] On the Kronecker canonical form of mixed matrix pencils (2011)
  • Author(s): S. Iwata and M. Takamatsu
  • Organizer: The 7th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: Kyoto
  • Year and Date: 2011-06-02
• [Presentation] On the Kronecker canonical form of mixed matrix pencils (2011)
  • Author(s): S.Iwata, M.Takamatsu
  • Organizer: The 7th Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-06-02
• [Presentation] On Kronecker canonical form of mixed matrix pencils(poster presentation) (2011)
  • Author(s): S. Iwata and M. Takamatsu
  • Organizer: SIAM Workshop on Combinatorial Scientific Computing(CSC11)
  • Place of Presentation: Darmstadt
  • Year and Date: 2011-05-19
• [Presentation] On Kronecker canonical form of mixed matrix pencils (2011)
  • Author(s): S.Iwata, M.Takamatsu
  • Organizer: SIAM Workshop on Combinatorial Scientific Computing (CSC11)
  • Place of Presentation: Darmstadium Conference Center
  • Year and Date: 2011-05-19
• [Presentation] 防犯センサを利用したオフィス内の人数推定 (2011)
  • Author(s): 高松瑞代, 田口東
  • Organizer: 日本オペレーションズ・リサーチ学会2011年春季研究発表会
  • Place of Presentation: 電気通信大学(調布市)
  • Year and Date: 2011-03-18
• [Presentation] 混合多項式行列の小行列式の最大次数を計算する組合せ緩和法 (2010)
  • Author(s): 岩田覚, 高松瑞代
  • Organizer: 日本オペレーションズ・リサーチ学会2010年秋季研究発表会
  • Place of Presentation: 福島
  • Year and Date: 2010-09-17
• [Presentation] 混合多項式行列の小行列式の最大次数を計算する組合せ緩和法 (2010)
  • Author(s): 岩田覚, 高松瑞代
  • Organizer: 日本オペレーションズ・リサーチ学会2010年秋季研究発表会
  • Place of Presentation: コラッセふくしま(福島市)
  • Year and Date: 2010-09-17
• [Remarks] 論文および発表
  • URL: http://www.ise.chuo-u.ac.jp/ise-labs/taguchi-lab/takamatsu/list.html
• [Remarks] 論文および発表
  • URL: http://www.misojiro.t.u-tokyo.ac.jp/~takamatu/list.html