Study of practical globally-convergent algorithms for solving large-scale nonlinear systems

• Project/Area Number: 20560369
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Communication/Network engineering
• Research Institution: Chuo University
• Principal Investigator: YAMAMURA Kiyotaka 中央大学, 理工学部, 教授 (30182603)
• Project Period (FY): 2008 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 非線形理論 / 回路 / 非線形数値解析 / 大規模集積回路 / 回路シミュレーション / 数理計画法 / 非線形理論・回路 / 全解探索 / 非線形システム / 非線形回路 / SPICE / 整数計画法

Research Abstract

In this project, we developed efficient and practical globally-convergent algorithms for solving large-scale nonlinear systems including large-scale integrated circuits. We first proposed an efficient homotopy method for solving nonlinear circuits, and

Research Products

• [Journal Article] Formulating hybrid equations and state equations for nonlinear circuits using SPICE (2013)
  • Author(s): K. Yamamura and M. Tonokura
  • Journal Title: International Journal of Circuit Theory and Applications Volume: vol.41, no.1 Pages: 101-110
  • Peer Reviewed
• [Journal Article] Finding all solutions of separable systems of piecewise-linear equations using integer programming (2012)
  • Author(s): K. Yamamura and N. Tamura
  • Journal Title: Journal of Computational and Applied Mathematics Volume: vol.236, issue 11 Pages: 2844-2852
  • Peer Reviewed
• [Journal Article] Finding all solutions of separable systems of piecewise-linear equations using integer programming (2012)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: Journal of Computational and Applied Mathematics Volume: (掲載決定) Issue: 11 Pages: 2844-2852
  • DOI: 10.1016/j.cam.2012.01.021
  • Peer Reviewed
• [Journal Article] 可変利得ホモトピー法を用いた非線形回路の直流動作点解析 (2012)
  • Author(s): 若木亮馬
  • Journal Title: 電子情報通信学会論文誌(A) Volume: J95-A Pages: 531-534
  • Peer Reviewed
• [Journal Article] The use of extrapolation in the computation of accurate numerical solutions of nonlinear two-point boundary value problems by the shooting method (2012)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: International Journal of Numerical Methods and Applications Volume: 8 Pages: 63-73
  • Peer Reviewed
• [Journal Article] Formulating hybrid equations and state equations for nonlinear circuits using SPICE (2012)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: International Journal of Circuit Theory and Applications Volume: (掲載決定) Issue: 1 Pages: 101-110
  • DOI: 10.1002/cta.788
  • Peer Reviewed
• [Journal Article] DC operating point analysis of transistor circuits using the variable-gain homotopy method (2012)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: Proceedings of International Technical Conference on Circuits/Systems, Computers and Communications Volume: 1
  • NAID: 130004770826
  • Peer Reviewed
• [Journal Article] Finding all solutions of piecewise-linear resistive circuits using separable programming (2012)
  • Author(s): Hideki Tanaka
  • Journal Title: Proceedings of 2012 IEEE Workshop on Nonlinear Circuit Networks Volume: 1 Pages: 67-70
  • Peer Reviewed
• [Journal Article] 一般化線形相補性理論と整数計画法を用いた区分的線形抵抗回路の完全解析 (2012)
  • Author(s): 加藤弘之
  • Journal Title: 第25回 回路とシステムワークショップ論文集 Volume: 1 Pages: 319-324
  • Peer Reviewed
• [Journal Article] 可変利得ホモトピー法を用いた非線形回路の直流動作点解析 (2012)
  • Author(s): 若木亮馬
  • Journal Title: 電子情報通信学会論文誌 Volume: Vol.J95-A(掲載決定)
  • Peer Reviewed
• [Journal Article] Quadratic convergence of the shooting method using implicit integration formulas and Newton's method (2011)
  • Author(s): K. Yamamura
  • Journal Title: International Journal of Numerical Methods and Applications Volume: vol.6,Issue 1 Pages: 87-104
  • Peer Reviewed
• [Journal Article] Quadratic convergence of the shooting method using implicit integration formulas and Newton's method (2011)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: International Journal of Numerical Methods and Applications Volume: Vol.6 Pages: 87-104
  • Peer Reviewed
• [Journal Article] Finding all solutions of piecewise-linear resistive circuits using integer programming (2011)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: Proceedings of 20th European Conference on Circuit Theory and Design (ECCTD 2011) Pages: 675-660
  • Peer Reviewed
• [Journal Article] DC analysis of piecewise-linear circuits using separable programming (2011)
  • Author(s): Hiroyuki Kato
  • Journal Title: Proceedings of the 2011 International Symposium on Nonlinear Theory and its Applications Pages: 274-277
  • Peer Reviewed
• [Journal Article] DC analysis of piecewise-linear circuits using separable programming (2011)
  • Author(s): Hiroyuki Kato
  • Journal Title: 第23回回路とシステム軽井沢ワークショップ論文集 Pages: 236-241
  • Peer Reviewed
• [Journal Article] 可変利得ニュートンホモトピー法を用いたMOSトランジスタ回路の直流動作点解析 (2010)
  • Author(s): 小山裕大
  • Journal Title: 電子情報通信学会論文誌 Volume: J93-A Pages: 840-843
  • Peer Reviewed
• [Journal Article] 整数計画法を用いた区分的線形回路の全解探索法 (2010)
  • Author(s): 上田恭大
  • Journal Title: 第23回回路とシステム軽井沢ワークショップ論文集 Pages: 17-22
  • Peer Reviewed
• [Journal Article] LP narrowing: A new strategy for finding all solutions of nonlinear equations (2009)
  • Author(s): K. Yamamura, K. Suda, and N. Tamura
  • Journal Title: Applied Mathematics and Computation Volume: vol.215, issue 1 Pages: 405-413
  • Peer Reviewed
• [Journal Article] An efficient and practical algorithm for finding all DC solutions of nonlinear circuits using GLPK (2009)
  • Author(s): K. Yamamura and K. Suda
  • Journal Title: IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences Volume: vol.E92-A, no.2 Pages: 638-642
  • NAID: 10026856016
  • Peer Reviewed
• [Journal Article] LP narrowing : A new strategy for finding all solutions of nonlinear equations (2009)
  • Author(s): K.Yamamura, K.Suda, N.Tamura
  • Journal Title: Applied Mathematics and Computation vol.215, issue 1 Pages: 405-413
  • Peer Reviewed
• [Journal Article] An efficient and practical algorithm for finding all DC solutions of nonlinear circuits using GLPK (2009)
  • Author(s): K.Yamamura, K.Suda
  • Journal Title: IEICE Trans.Fundamentals of Electronics, Communications and Computer Sciences vol.E92-A, no.2 Pages: 638-642
  • NAID: 10026856016
  • Peer Reviewed
• [Journal Article] An efficient algorithm for finding all DC solutions of piecewise-linear circuits (2009)
  • Author(s): 山村清隆
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E92-A・2 Pages: 638-642
  • NAID: 110003292601
  • Peer Reviewed
• [Journal Article] LP narrowing : A new strategy for finding all solutions of nonlinear equations (2009)
  • Author(s): 山村清隆
  • Journal Title: Applied Mathematics and Computation 215・1 Pages: 405-413
  • Peer Reviewed
• [Journal Article] An efficient algorithm for finding all DC solutions of nonlinear circuits using LP narrowing (2009)
  • Author(s): 山村清隆
  • Journal Title: Proceedings 2009 IEEE International Symposium on Circuits and Systems Pages: 2081-2084
  • Peer Reviewed
• [Journal Article] A globally convergent variable-gain homotopy method for solving modified nodal equations (2009)
  • Author(s): Kazuma Watanabe
  • Journal Title: Proceedings of 2009 International Symposium on Nonlinear Theory and its Applications Pages: 507-510
  • Peer Reviewed
• [Journal Article] Formulating hybrid equations for nonlinear circuits using SPICE (2009)
  • Author(s): 戸野倉充
  • Journal Title: Proceedings of 2009 International Symposium on Nonlinear Theory and its Applications Pages: 515-518
  • Peer Reviewed
• [Journal Article] Finding all DC solutions of piecewise-linear circuits using integer programming (2009)
  • Author(s): 山村清隆
  • Journal Title: Proceedings of 2009 IEEE Workshop on Nonlinear Circuit Networks Pages: 37-40
  • NAID: 110007387521
  • Peer Reviewed
• [Journal Article] SPICEの過渡解析による非線形抵抗回路の混合方程式の導出 (2009)
  • Author(s): 戸野倉充
  • Journal Title: 第22回 回路とシステム軽井沢ワークショップ論文集 Pages: 13-18
  • Peer Reviewed
• [Journal Article] 数理計画法の非線形回路解析への応用 (2009)
  • Author(s): 山村清隆
  • Journal Title: 第22回 回路とシステム軽井沢ワークショップ論文集 Pages: 264-269
  • Peer Reviewed
• [Journal Article] 整数計画法を用いた区分的線形回路の全解探索法 (2009)
  • Author(s): 田村直也
  • Journal Title: 電子情報通信学会技術研究報告 NLP2009-68 Pages: 47-52
• [Journal Article] 可変利得ニュートンホモトピー法を用いたMOSトランジスタ回路の直流動作点解析 (2009)
  • Author(s): 小山裕大
  • Journal Title: 電子情報通信学会技術研究報告 NLP2009-137 Pages: 59-64
• [Journal Article] GLPKを用いた区分的線形回路の全解探索法 (2009)
  • Author(s): 田村直也
  • Journal Title: 電子情報通信学会技術研究報告 NLP2009-14 Pages: 25-30
• [Journal Article] An efficient and practical algorithm for finding all DC solutions of nonlinear circuits using GLPK (2009)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E92-A・2 Pages: 638-642
  • NAID: 10026856016
  • Peer Reviewed
• [Journal Article] An efficient algorithm for finding all dc solutions of nonlinear circuitsusing LP narrowing (2009)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: Proceedings of IEEE 2007 International Symposium on Circuits and Systems (掲載決定)
  • Peer Reviewed
• [Journal Article] SPICEの過渡解析による非線形抵抗回路の混合方程式の導出 (2009)
  • Author(s): 戸野倉充
  • Journal Title: 第22回回路とシステム軽井沢ワークショップ論文集 (掲載決定)
  • Peer Reviewed
• [Journal Article] 数理計画法の非線形回路解析への応用(招待論文) (2009)
  • Author(s): 山村清隆
  • Journal Title: 第22回回路とシステム軽井沢ワークショップ論文集 (掲載決定)
• [Journal Article] DC tolerance analysis of nonlinear circuits using set-valued functions (2008)
  • Author(s): K. Yamamura and Y. Haga
  • Journal Title: Journal of Circuits, Systems, andComputers Volume: vol.17, no.5 Pages: 785-796
  • NAID: 110006457303
  • Peer Reviewed
• [Journal Article] An efficient algorithm for finding all DC solutions of piecewise-linear circuits (2008)
  • Author(s): K. Yamamura and A. Machida
  • Journal Title: International Journal of Circuit Theory and Applications Volume: vol.36, no.8 Pages: 989-1000
  • NAID: 110003292601
  • Peer Reviewed
• [Journal Article] DC tolerance analysis of nonlinear circuits using set-valued functions (2008)
  • Author(s): K.Yamamura, Y.Haga
  • Journal Title: J.Circuits, Systems, and Computers vol.17, no.5 Pages: 785-796
  • NAID: 110006457303
  • Peer Reviewed
• [Journal Article] An efficient algorithm for finding all DC solutions of piecewise-linear circuits (2008)
  • Author(s): K.Yamamura, A.Machida
  • Journal Title: International Journal of Circuit Theory and Applications vol.36, no.8 Pages: 989-1000
  • NAID: 110003292601
  • Peer Reviewed
• [Journal Article] ネットリストによる混合方程式の導出 (2008)
  • Author(s): 山村清隆, 須田広紀
  • Journal Title: 電子情報通信学会論文誌(A) vol.J91-A, no.7 Pages: 739-743
  • NAID: 110006344211
  • Peer Reviewed
• [Journal Article] ネットリストによる混合方程式の導出 (2008)
  • Author(s): 山村清隆
  • Journal Title: 電子情報通信学会論文誌(A) J91-A・7 Pages: 739-743
  • NAID: 110006344211
  • Peer Reviewed
• [Journal Article] DC tolerance analysis of nonlinear circuits using set-valued functions (2008)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: Journal of Circuits, Systems, and Computers 17・5 Pages: 785-796
  • NAID: 110006457303
  • Peer Reviewed
• [Journal Article] An efficient algorithm for finding all DC solutions of piecewise-linearcircuits (2008)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: International Journal of Circuit Theory and Applications 36・8 Pages: 989-1000
  • NAID: 110003292601
  • Peer Reviewed
• [Journal Article] LP narrowing : A new strategy for finding all solutions of nonlinear equations (2008)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: Book of Abstracts, 13th GAMM-IMACS International Symposium on SCAN E92-A・2 Pages: 149-150
  • Peer Reviewed
• [Journal Article] LP narrowing : 非線形回路の新しい全解探索法 (2008)
  • Author(s): Naoya Tamura
  • Journal Title: 第21回 回路とシステム軽井沢ワークショップ論文集 Pages: 1-6
  • Peer Reviewed
• [Journal Article] An efficient algorithm for finding all DC solutions of piecewise-linearcircuits (2008)
  • Author(s): Kiyotaka Yamamura
  • Journal Title: 電子情報通信学会技術研究報告 NLP2007-166 Pages: 71-76
  • NAID: 110003292601
• [Journal Article] LP縮小を用いた大規模非線形方程式の全解探索法 (2008)
  • Author(s): 山村清隆
  • Journal Title: 第37回数値解析シンポジウム講演予稿集 Pages: 33-36
• [Journal Article] SPICEによる混合方程式の導出 (2008)
  • Author(s): 山村情隆
  • Journal Title: 電子情報通信学会技術研究報告 NLP2007-55 Pages: 53-57
  • NAID: 110007086927
• [Presentation] Finding all solutions of piecewiselinear resistive circuits using separable programming (2012)
  • Author(s): H. Tanaka, H. Kato, and K. Yamamura
  • Organizer: Proceedings of 2012 IEEE Workshop on Nonlinear Circuit Networks
  • Place of Presentation: Tokushima, Japan
  • Year and Date: 2012-12-15
• [Presentation] DC operating point analysis oftransistor circuits using the variable-gain homotopy method (2012)
  • Author(s): K. Yamamura and T. Miyamoto
  • Organizer: Proceedings of InternationalTechnical Conference on Circuits/Systems, Computers and Communications
  • Year and Date: 2012-07-17
• [Presentation] アフィン演算とLP縮小を用いた非線形回路の全解探索法 (2012)
  • Author(s): 小林玄宙
  • Organizer: 電子情報通信学会総合大会
  • Place of Presentation: 岡山大学
  • Year and Date: 2012-03-20
• [Presentation] SPICEを用いた非線形回路の状態方程式の導出 (2011)
  • Author(s): 久保田新悟
  • Organizer: 電子情報通信学会ソサイエティ大会
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-09-13
• [Presentation] Finding all solutions of piecewiselinear resistive circuits usinginteger programming (2011)
  • Author(s): K. Yamamura and T. Ueda
  • Organizer: Proceedings of 20th IEEE European Conference on Circuit Theory and Design
  • Place of Presentation: Linkoping, Sweden
  • Year and Date: 2011-08-30
• [Presentation] SPICEを用いた区分的線形回路の全解探索法 (2010)
  • Author(s): 加藤弘之
  • Organizer: 電子情報通信学会ソサイエティ大会
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2010-09-14
• [Presentation] Verilog-A を用いたホモトピー法の実装 (2010)
  • Author(s): 松本廉太郎
  • Organizer: 電子情報通信学会総合大会
  • Place of Presentation: 東北大学
  • Year and Date: 2010-03-16
• [Presentation] Finding all DC solutions ofpiecewise-linear circuits usinginteger programming (2009)
  • Author(s): K. Yamamura, N. Tamura, and T. Ueda
  • Organizer: Proceedings of 2009 IEEE Workshop on Nonlinear Circuit Networks
  • Place of Presentation: Tokushima, Japan
  • Year and Date: 2009-12-11
• [Presentation] Finding all DC solutions of piecewise-inear circuits using integer programming (2009)
  • Author(s): K.Yamamura, N.Tamura, T.Ueda
  • Organizer: 2009 IEEE Workshop on Nonlinear Circuit Networks
  • Place of Presentation: Tokushima, Japan
  • Year and Date: 2009-12-11
• [Presentation] Formulating hybrid equations for nonlinear circuits using SPICE (2009)
  • Author(s): M.Tonokura, K.Yamamura
  • Organizer: 2009 International Symposium on Nonlinear Theory and its Applications
  • Place of Presentation: Sapporo, Japan
  • Year and Date: 2009-10-20
• [Presentation] A globally convergent variable-gain homotopy method for solving modified nodal equations (2009)
  • Author(s): K.Watanabe K.Yamamura
  • Organizer: 2009 International Symposium on Nonlinear Theory and its Applications(507-510)
  • Place of Presentation: Sapporo, Japan
  • Year and Date: 2009-10-20
• [Presentation] An efficient algorithm for finding all DC solutions of nonlinear circuits using LP narrowing (2009)
  • Author(s): K. Yamamura, N. Tamura, and K. Suda
  • Organizer: Proceedings of 2009 IEEE International Symposium on Circuits and Systems
  • Place of Presentation: Taipei, Taiwan
  • Year and Date: 2009-05-26
• [Presentation] An efficient algorithm for finding all DC solutions of nonlinear circuits using LP narrowing (2009)
  • Author(s): K.Yamamura, N.Tamura, K.Suda
  • Organizer: IEEE 2009 International Symposium on Circuits and Systems(2081-2084)
  • Place of Presentation: Taipei, Taiwan
  • Year and Date: 2009-05-26
• [Presentation] 数理計画法の非線形回路解析への応用 (2009)
  • Author(s): 山村清隆
  • Organizer: 電子情報通信学会 第22回 回路とシステム軽井沢ワークショップ
  • Place of Presentation: 軽井沢プリンスホテル
  • Year and Date: 2009-04-21
• [Presentation] LP narrowing: A new strategy for finding all solutions of nonlinear equations (2008)
  • Author(s): K. Yamamura, N. Tamura, and K. Suda
  • Organizer: Book of Abstracts, 13th GAMM -- IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics
  • Year and Date: 2008-09-30
• [Presentation] LP narrowing : A new strategy for finding all solutions of nonlinear equations (2008)
  • Author(s): K.Yamamura, N.Tamura, K.Suda
  • Organizer: 13th GAMM--IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics(149-150)
  • Year and Date: 2008-09-30
• [Presentation] SCIPを用いた区分的線形回路の全解探索法
  • Author(s): 山村清隆
  • Organizer: 電子情報通信学会回路とシステム研究会
  • Place of Presentation: 京都
• [Presentation] 一般化線形相補性理論と混合整数計画法を用いた区分的線形抵抗回路の完全解析
  • Author(s): 前田礼維
  • Organizer: 電子情報通信学会非線形問題研究会
  • Place of Presentation: 神戸