Validate Computation Library on Time Evolution Equations

• Project/Area Number: 21540115
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: The University of Electro-Communications
• Principal Investigator: YAMAMOTO Nobito 電気通信大学, 大学院・情報理工学研究科, 教授 (30210545)
• Co-Investigator(Kenkyū-buntansha): NAKAMURA Ken-ichi 金沢大学, 理工研究域数物科学系, 准教授 (40293120) ; OGATA Hidenori 電気通信大学, 大学院・情報理工学研究科, 准教授 (50242037)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 精度保証 / 発展方程式 / 多倍長演算 / プログラム自動生成 / 常微分方程式 / 微分方程式 / 力学系 / 自動プログラミング / 区間解析 / 計算ライブラリ

Research Abstract

We have investigated in computer program library including validated computation techniques which give the basis of validated computation of time evolution equations, and derived a number of new approaches to numerical verification of ODEs which appear as semi-discretized equations of PDEs. The results were published in academic journals.

Research Products

• [Journal Article] Validated Computation of Global Solutions to ODEs (2013)
  • Author(s): M. Harikae, N. Yamamoto
  • Journal Title: Nonlinear Theory and Its Applications, IEICE Volume: Vol.4, No.1 Pages: 88-96
  • NAID: 130003375414
  • URL: http://dx.doi.org/10.1587/nolta.4.88
• [Journal Article] 力学系における閉軌道の存在領域の精度保証法による同定 (2012)
  • Author(s): 樋脇知広・山本野人
  • Journal Title: 日本応用数理学会論文誌 Volume: Vol.22, No.4 Pages: 269-276
• [Journal Article] On the basic operations of interval multiple-precision arithmetic with center-radius form (2011)
  • Author(s): N. Matsuda, N. Yamamoto
  • Journal Title: Nonlinear Theory and Its Applications, IEICE Volume: Vol.2, No.1 Pages: 54-67
  • NAID: 130000903442
  • URL: http://dx.doi.org/10.1587/nolta.2.54
• [Journal Article] On the basic operations of interval multiple-precision arithmetic with center-radius form (2011)
  • Author(s): N.Matsuda, N.Yamamoto
  • Journal Title: Nonlinear Theory and Its Applications Volume: 2 Pages: 54-67
  • NAID: 130000903442
  • Peer Reviewed
• [Journal Article] A Theorem for Numerical Verification on Local Uniqueness of Solutionsto Fixed-Point Equations (2011)
  • Author(s): N.Yamamoto, M.T.Nakao, Y.Watanabe
  • Journal Title: Numerical Functional Analysis and Optimization Volume: 32 Pages: 1190-1204
  • Peer Reviewed
• [Journal Article] 精度保証付き多倍長演算の方法と構成 (2010)
  • Author(s): 山W本野人・松田望
  • Journal Title: 計測と制御 Volume: 49 Pages: 297-302
  • Peer Reviewed
• [Journal Article] An Application of Taylor Models to the Nakao Method on ODEs (2009)
  • Author(s): N.Yamamoto, T.Komori
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 26, No.1 Pages: 365-392
  • NAID: 10028169196
• [Journal Article] An Application of Taylor Models to the Nakao Method on ODEs (2009)
  • Author(s): Nobito Yamamoto, Takashi Komori
  • Journal Title: Japan Journal of Industrial and Applied Mathematics 26 Pages: 365-392
  • NAID: 10028169196
  • Peer Reviewed
• [Presentation] 常微分方程式の大域解に対する精度保証付き数値計算 (2011)
  • Author(s): 張替将人、山本野人
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-10-01
• [Presentation] MATLAB上の数式処理を用いた精度保証付き計算プログラムの自働生成 (2011)
  • Author(s): 宇川隆詞、山本野人
  • Organizer: 日本応用数理学会2011年研究部会連合発表会
  • Place of Presentation: 電気通信大学
  • Year and Date: 2011-03-08
• [Presentation] Validated Computation of Global Solutions to ODEs (2011)
  • Author(s): N. Yamamoto, M. Harikae
  • Organizer: the Japan-German Workshop on Computer-Assisted proofs and Verification Methods
  • Place of Presentation: Karisruhe,Germany
• [Presentation] MATLABの数式処理機能による精度保証計算プログラムの自動生成 (2010)
  • Author(s): 宇川隆詞、山本野人
  • Organizer: 2010年度応用数学合同研究集会
  • Place of Presentation: 龍谷大学
  • Year and Date: 2010-12-18
• [Presentation] 精度保証付き多倍長演算の実装について (2010)
  • Author(s): 山本野人、松田望
  • Organizer: 日本応用数理学会2010年度年会
  • Place of Presentation: 明治大学
  • Year and Date: 2010-09-07
• [Presentation] 精度保証付き多倍長並列演算環境の構築と計算機援用解析への展開 (2010)
  • Author(s): 山本野人、松田望、渡部善隆、藤原宏志
  • Organizer: 学際大規模情報基盤共同利用・共同研究拠点第1回シンポジウム
  • Place of Presentation: 東京大学
  • Year and Date: 2010-09-01
• [Presentation] 「常微分方程式の精度保証付き計算の技法と利用法」(招待講演) (2010)
  • Author(s): 山本野人
  • Organizer: 天体力学N体力学研究会・ちばN体2010
  • Place of Presentation: 千葉大学
  • Year and Date: 2010-03-19
• [Presentation] ODEに対する精度保証プログラム生成の半自動化について (2010)
  • Author(s): 宇川隆詞, 山本野人
  • Organizer: 日本応用数理学会2010年 研究部会 連合発表会
  • Place of Presentation: 筑波大学
  • Year and Date: 2010-03-08
• [Presentation] Interval Multiple-Precision Arithmetic with center-radius form (2010)
  • Author(s): N. Yamamoto, N. Matsuda
  • Organizer: SCAN2010, 14th GAMM-IMACS, International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics
  • Place of Presentation: ENS de Lyon, Francs
• [Presentation] Interval multiple-precision arithmetic with center-radius form (2010)
  • Author(s): N.Yamamoto, N.Matsuda
  • Organizer: SCAN2010
  • Place of Presentation: ENS de Lyon, France
• [Presentation] 多倍長演算の精度保証について (2009)
  • Author(s): 松田望、山本野人
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学
  • Year and Date: 2009-12-17
• [Presentation] Construction of an automatic validated computation for boundary value problems of ODEs' (2009)
  • Author(s): Nobito Yamamoto, Ryuji Ukawa, Nozomu Matsuda
  • Organizer: ASCM-MACIS2009
  • Place of Presentation: 九州大学
  • Year and Date: 2009-12-15
• [Presentation] On Validated Computation with Multipleprecision Arithmetic (2009)
  • Author(s): 山本野人
  • Organizer: Taiwan-Japan Joint Seminar
  • Place of Presentation: 台湾大学、中華民国、台北
  • Year and Date: 2009-11-07
• [Presentation] 「精度保証付き数値計算と多倍長演算」(招待) (2009)
  • Author(s): 山本野人
  • Organizer: デジタル解析学セミナー
  • Place of Presentation: 早稲田大学
  • Year and Date: 2009-10-19
• [Presentation] An application of the Lohner method for boundary value problems of ODEs' (2009)
  • Author(s): Nobito Yamamoto, Ryuji Ukawa, Nozomu Matsuda
  • Organizer: ECM2009
  • Place of Presentation: 香港理工大学、中華人民共和国、香港
  • Year and Date: 2009-05-26
• [Book] 「精度保証の手法」、現代数理科学事典第2 版IX 章第6節 (2009)
  • Author(s): 山本野人
  • Publisher: 丸善
• [Book] 第2版 現代数理科学事典 (2009)
  • Author(s): 広中平祐編・山本野人, ほか著
  • Total Pages: 1080
  • Publisher: 丸善出版