On the Study of Highly Reliable Symbolic-Numeric Computation for Algebraic Problems with Empirical Data

• Project/Area Number: 21500026
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: Tokai University (2010-2011); NTT Communication Science Laboratories (2009)
• Principal Investigator: SEKIGAWA Hiroshi 東海大学, 理学部, 准教授 (00396178)
• Co-Investigator(Kenkyū-buntansha): SHIRAYANAGI Kioshi 東邦大学, 理学部, 教授 (80396176)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: 多項式 / 代数方程式 / 誤差 / 数値数式融合計算 / 安定化理論 / 連立代数方程式 / 近似 / 零点 / 根 / 凸包構成 / 整除性 / グレブナ基底

Research Abstract

We proposed highly reliable symbolic-numeric computation methods for algebraic problems with empirical data. Some main results are as follows.(1) An algorithm to determine divisibility of polynomials.(2) A new application of stabilization techniques.(3) An algorithm to compute the maximal perturbations for preserving properties of solutions of a polynomial system. Furthermore, we analyzed computing time to find a real univariate polynomial that has a zero in a given complex domain and is nearest to a given real univariate polynomial.

Research Products

• [Journal Article] Computing the Nearest Polynomial with a Zero in a Given Domain by using Piecewise Rational Functions (2011)
  • Author(s): H. Sekigawa
  • Journal Title: Journal of Symbolic Computation Volume: Vol.46 Issue 12 Pages: 1318-1335
• [Journal Article] Isolated Real Zero of a Real Polynomial System under Perturbation (2011)
  • Author(s): H. Sekigawa and K. Shirayanagi
  • Journal Title: ACM Communications in Computer Algebra Volume: Vol.45, No.2 Pages: 131-132
  • Peer Reviewed
• [Journal Article] Isolated Real Zero of a Real Polynomial System under Perturbation (2011)
  • Author(s): Hiroshi Sekigawa, Kiyoshi Shirayanagi
  • Journal Title: ACM Communications in Computer Algebra Volume: 45 Pages: 131-132
  • Peer Reviewed
• [Journal Article] Computing the Nearest Polynomial with a Zero in a Given Domain by using Piecewise Rational Functions (2011)
  • Author(s): Hiroshi Sekigawa
  • Journal Title: Journal of Symbolic Computation Volume: 46 Issue: 12 Pages: 1318-1335
  • DOI: 10.1016/j.jsc.2011.08.012
  • Peer Reviewed
• [Journal Article] Solvability of Bivariate Polynomial Systems under Perturbation (2010)
  • Author(s): H. Sekigawa and K. Shirayanagi
  • Journal Title: ACM Communications in Computer Algebra Volume: Vol.44, No.3 Pages: 147-148
  • Peer Reviewed
• [Journal Article] Solvability of Bivariate Polynomial Systems under Perturbation (2010)
  • Author(s): Hiroshi Sekigawa, Kiyoshi Shirayanagi
  • Journal Title: ACM Communications in Computer Algebra Volume: 44 Pages: 147-148
  • Peer Reviewed
• [Journal Article] A Sequence of Nearest Polynomials with Given Factors (2009)
  • Author(s): H. Sekigawa
  • Journal Title: Math-for-Industry Lecture Note Volume: Vol.22 Pages: 187-190
  • Peer Reviewed
• [Journal Article] Reducing Exact Computations to Obtain Exact Results Based on Stabilization Techniques (2009)
  • Author(s): K. Shirayanagi and H. Sekigawa
  • Journal Title: Proceedings of International Workshop on Symbolic-Numeric Computation 2009 Pages: 191-197
  • Peer Reviewed
• [Journal Article] A New Method of Reducing Exact Computations to Obtain Exact Results (2009)
  • Author(s): K. Shirayanagi and H. Sekigawa
  • Journal Title: ACM Communications in Computer Algebra Volume: Vol.43, No.3 Pages: 102-104
  • Peer Reviewed
• [Journal Article] Deciding Divisibility between Polynomials with Inexact Coefficients (2009)
  • Author(s): H. Nakayama and H. Sekigawa
  • Journal Title: ACM Communications in Computer Algebra Volume: Vol.43, No.3 Pages: 91-94
  • NAID: 110007123964
  • Peer Reviewed
• [Journal Article] Reducing Exact Computations to Obtain Exact Results Based on Stabilization Techniques (2009)
  • Author(s): Kiyoshi Shirayanagi
  • Journal Title: Proceedings of SNC'09(Symb. Numer. Comput.) Pages: 191-197
  • Peer Reviewed
• [Journal Article] A Sequence of Nearest Polynomials with Given Factors (2009)
  • Author(s): Hiroshi Sekigawa
  • Journal Title: Math-for-Industry Lecture Note Vol.22 Pages: 187-190
  • Peer Reviewed
• [Presentation] 連立代数方程式の解の個数を保つ摂動限界 (2012)
  • Author(s): 関川浩, 白柳潔
  • Organizer: Risa/Asir Conference
  • Place of Presentation: 神戸大学(神戸市)
  • Year and Date: 2012-03-20
• [Presentation] 連立代数方程式の解の個数を保つ摂動限界 (2012)
  • Author(s): 関川浩, 白柳潔
  • Organizer: Risa/Asir Conference 2012
  • Place of Presentation: 神戸大学(神戸市)
  • Year and Date: 2012-03-20
• [Presentation] 係数に誤差のある実係数連立代数方程式の孤立実数解について (2011)
  • Author(s): 関川浩, 白柳潔
  • Organizer: Risa/Asir Conference
  • Place of Presentation: 神戸大学(神戸市)
  • Year and Date: 2011-03-21
• [Presentation] 係数に誤差のある実係数連立代数方程式の孤立実数解について (2011)
  • Author(s): 関川浩, 白柳潔
  • Organizer: Risa/Asir Conference 2011
  • Place of Presentation: 神戸大学(神戸市)
  • Year and Date: 2011-03-21
• [Presentation] Isolated Real Zero of a Real Polynomial System under Perturbation (2011)
  • Author(s): H. Sekigawa and K. Shirayanagi
  • Organizer: International Symposium on Symbolic and Algebraic Computation 2011
  • Place of Presentation: サンノゼコンベンションセンター(米国)
• [Presentation] 安定化理論に基づくISCZ法の凸包構成への応用,京都大学数理解析研究所研究集会 (2010)
  • Author(s): 白柳潔, 関川浩
  • Organizer: Computer Algebra-Design of Algorithms, Implementations and Applications
  • Place of Presentation: 京都大学(京都市)
  • Year and Date: 2010-12-03
• [Presentation] 安定化理論に基づくISCZ法の凸包構成への応用 (2010)
  • Author(s): 白柳潔, 関川浩
  • Organizer: 京都大学数理解析研究所研究集会Computer Algebra-Design of Algorithms, Implementations and Applications
  • Place of Presentation: 京都大学(京都市)
  • Year and Date: 2010-12-03
• [Presentation] 係数に誤差のある連立代数方程式の可解性について (2010)
  • Author(s): 関川浩, 白柳潔
  • Organizer: 第19回日本数式処理学会大会
  • Place of Presentation: 名古屋大学(名古屋市)
  • Year and Date: 2010-06-13
• [Presentation] Solvability of Bivariate Polynomial Systems under Perturbation (2010)
  • Author(s): H. Sekigawa and K. Shirayanagi
  • Organizer: International Symposium on Symbolic and Algebraic Computation 2010
  • Place of Presentation: ミュンヘン工科大学(ドイツ)
• [Presentation] A Sequence of Nearest Polynomials with Given Factors (2009)
  • Author(s): H. Sekigawa
  • Organizer: The 9th Asian Symposium on Computer Mathematics and the 3rd International Conference on Mathematical Aspects of Computer and Information Sciences
  • Place of Presentation: JALリゾートシーホークホテル福岡(福岡市)
  • Year and Date: 2009-12-14
• [Presentation] A Sequence of Nearest Polynomials with Given Factors (2009)
  • Author(s): Hiroshi Sekigawa
  • Organizer: The 9th Asian Symposium on Computer Mathematics and the 3rd International Conference on Mathematical Aspects of Computer and Information Sciences
  • Place of Presentation: JALリゾート シーホークホテル福岡(福岡市)
  • Year and Date: 2009-12-14
• [Presentation] 安定化理論に基づくISCZ法の有効性について,京都大学数理解析研究所研究集会 (2009)
  • Author(s): 白柳潔, 関川浩
  • Organizer: Computer Algebra-Design of Algorithms, Implementations and Applications
  • Place of Presentation: 京都大学(京都市)
  • Year and Date: 2009-11-04
• [Presentation] 安定化理論に基づくISCZ法の有効性について (2009)
  • Author(s): 白柳潔
  • Organizer: 京都大学数理解析研究所研究集会 Computer Algebra-Design of Algorithms, Implementations and Applications
  • Place of Presentation: 京都大学(京都市)
  • Year and Date: 2009-11-03
• [Presentation] Reducing Exact Computations to Obtain Exact Results Based on Stabilization Techniques (2009)
  • Author(s): K. Shirayanagi and H. Sekigawa
  • Organizer: The 3^<rd> International Symposium on Symbolic and Algebraic Computation
  • Place of Presentation: コープイン京都(京都市)
  • Year and Date: 2009-08-03
• [Presentation] Reducing Exact Computations to Obtain Exact Results Based on Stabilization Techniques (2009)
  • Author(s): Kiyoshi Shirayanagi
  • Organizer: The 3rd International Workshop on Symbolic-Numeric Computation
  • Place of Presentation: コープイン京都(京都市)
  • Year and Date: 2009-08-03
• [Presentation] A New Method of Reducing Exact Computations to Obtain Exact Results (2009)
  • Author(s): K. Shirayanagi and H. Sekigawa
  • Organizer: International Symposium on Symbolic and Algebraic Computation2009
  • Place of Presentation: Korea Institute for Advanced Study(韓国)
  • Year and Date: 2009-07-30
• [Presentation] Deciding Divisibility between Polynomials with Inexact Coefficients (2009)
  • Author(s): H. Nakayama and H. Sekigawa
  • Organizer: International Symposium on Symbolic and Algebraic Computation2009
  • Place of Presentation: Korea Institute for Advanced Study(韓国)
  • Year and Date: 2009-07-30
• [Presentation] Deciding Divisibility between Polynomials with Inexact Coefficients (2009)
  • Author(s): Hiroki Nakayama
  • Organizer: The 2009 International Symposium on Symbolic and Algebraic Computation
  • Place of Presentation: Korea Institute for Advanced Study(Korea)
  • Year and Date: 2009-07-30
• [Presentation] A New Method of Reducing Exact Computations to Obtain Exact Results (2009)
  • Author(s): Kiyoshi Shirayanagi
  • Organizer: The 2009 International Symposium on Symbolic and Algebraic Computation
  • Place of Presentation: Korea Institute for Advanced Study(Korea)
  • Year and Date: 2009-07-30
• [Patent(Industrial Property Rights)] 連立代数方程式の係数に対する許容誤差限界評価装置、方法、プログラム (2010)
  • Inventor(s): 関川浩
  • Industrial Property Rights Holder: 日本電信電話株式会社
  • Industrial Property Number: 2010-059763
  • Filing Date: 2010-03-16
• [Patent(Industrial Property Rights)] 最近多項式算出装置、方法及びプログラム (2009)
  • Inventor(s): 関川浩
  • Industrial Property Rights Holder: 日本電信電話株式会社
  • Industrial Property Number: 2009-277454
  • Filing Date: 2009-12-07
• [Patent(Industrial Property Rights)] 最近多項式算出装置、方法びプログラム (2009)
  • Inventor(s): 関川浩
  • Industrial Property Rights Holder: 日本電信電話株式会社
  • Industrial Property Number: 2009-277454
  • Filing Date: 2009-12-07