Numerical Analysis of Inverse Problems using High-Accurate Regularization and Next-Generation Computing Environments

• Project/Area Number: 20740057
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyoto University
• Principal Investigator: FUJIWARA Hiroshi Kyoto University, 大学院・情報学研究科, 助教 (00362583)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 多倍長計算 / 高精度数値計算 / 数値的不安定性 / 非適切問題 / 正則化法 / Laplace逆変換 / 逆問題 / Laplace実逆変換 / 数値解析 / 再生Hilbert空間 / 再生核Hilbert空間

Research Abstract

We have developed a multiple-precision arithmetic environment, and realized a high-accurate numerical computation for numerically unstable problems using the environment. The developed software is distributed via Internet. It is designed for scientific numerical computation. We also give some remarks on floating-point arithmetic and numerical stability.

Research Products

• [Journal Article] 輸送方程式の散乱核の等方性・異方性と数値解の挙動 (2011)
  • Author(s): 藤原宏志, 東森信就
  • Journal Title: 第60回理論応用力学講演会講演論文集
  • NAID: 130004604675
• [Journal Article] 複素逆Laplace変換の数値計算における注意 (2010)
  • Author(s): 藤原宏志
  • Journal Title: 計算数理工学論文集 Vol.10 Pages: 7-10
  • NAID: 40018997674
  • Peer Reviewed
• [Journal Article] 科学技術計算のための高速多倍長計算環境の構築 (2010)
  • Author(s): 藤原宏志
  • Journal Title: 計測自動制御学会(SICE)計測と制御5 Vol.49 Pages: 285-290
  • NAID: 10026206930
• [Journal Article] Numerical Real Inversion of the Laplace Transform by Reproducing Kernel and Multiple-Precision Arithmetic (2010)
  • Author(s): H.Fujiwara
  • Journal Title: PROGRESS IN ANALYSIS AND ITS APPLICATIONS Pages: 289-295
  • Peer Reviewed
• [Journal Article] 複素逆Llaplace変換の数値計算における注意 (2010)
  • Author(s): 藤原宏志
  • Journal Title: 計算数理工学論文集 Volume: Vol.10 Pages: 7-10
  • Peer Reviewed
• [Journal Article] Numerical Real Inversion of the Laplace Transform by Reproducing Kernel and Multiple-Precision Arithmetic (2010)
  • Author(s): H.Fujiwara
  • Journal Title: Proceedings of the 7th international ISAAC congress Pages: 289-295
  • Peer Reviewed
• [Journal Article] 科学技術計算のための高速多倍長計算環境の構築 (2010)
  • Author(s): 藤原宏志
  • Journal Title: 計測自動制御学会(SICE)計測と制御 Volume: Vol.49,5 Pages: 285-290
  • NAID: 10026206930
• [Journal Article] 多倍長計算による非適切問題の大規模高精度計算の実現に向けて (2010)
  • Author(s): 藤原宏志
  • Journal Title: 第22回RAMPシンポジウム論文集 Pages: 183-194
• [Journal Article] PC・クラスタ向きの高速多倍長計算環境の構築と科学技術計算への応用 (2010)
  • Author(s): 藤原宏志
  • Journal Title: 計算工学講演会論文集 Pages: 887-890
  • NAID: 40019577192
• [Journal Article] Banach scale上の差分法の多倍長数値計算環境での実現 (2010)
  • Author(s): 磯祐介, 藤原宏志, 西田詩
  • Journal Title: 第59回理論応用力学講演会 講演論文集 Pages: 363-364
  • NAID: 130004604538
• [Journal Article] Numerical real inversion of the Laplace transform by using a high-accuracy numerical method (2009)
  • Author(s): H.Fujiwara, T.Matsuura, S.Saitoh, Y.Sawano
  • Journal Title: Proceedings of the 6th International ISAAC Congress Pages: 574-583
  • Peer Reviewed
• [Journal Article] Finite Difference Approximation of Ill-Posed Cauchy Problems (2009)
  • Author(s): Kotoba NISHIDA, Hiroshi FUJIWARA, Yuusuke ISO
  • Journal Title: Theoretical and Applied Mechanics Japan 57 Pages: 405-410
  • NAID: 130004463704
  • Peer Reviewed
• [Journal Article] 熱方程式の境界値逆問題の解の再構成について (2009)
  • Author(s): 藤原宏志, 磯祐介
  • Journal Title: 第58回理論応用力学講演会 講演論文集 Pages: 483-484
  • NAID: 130004604323
• [Journal Article] 再生核Hilbert空間上のTikhonov正則化法とLaplace実逆変換の数値計算への応用 (2009)
  • Author(s): 藤原宏志, 東森信就
  • Journal Title: 数理解析研究所講究録 1638 Pages: 137-145
• [Journal Article] 数値的に不安定な線型問題のための多倍長精度・並列直接解法ライブラリの開発 (2008)
  • Author(s): 藤原宏志
  • Journal Title: 計算数理工学論文集 Vol.8 Pages: 49-52
  • Peer Reviewed
• [Journal Article] Real inversion formulas of the Laplace transform on weighted function spaces (2008)
  • Author(s): Y. Sawano, H. Fujiwara, and S. Saitoh
  • Journal Title: Complex Anal. Oper. Theory Vol.2, No.3 Pages: 511-521
  • Peer Reviewed
• [Journal Article] 数値的に不安定な焔型問題のための多倍長精度・並列直接解法ライブラリの開発 (2008)
  • Author(s): 藤原宏志
  • Journal Title: 計算数理工学論文集 Vol.8 Pages: 49-52
  • Peer Reviewed
• [Journal Article] Numerical Real Inversion Formulas of the Laplace Transform and their Applications (2008)
  • Author(s): 藤原宏志
  • Journal Title: 数理解析研究所講究録 1618 Pages: 192-209
• [Journal Article] ラプラス変換の実逆変換への再生核空間の応用 (2008)
  • Author(s): 澤野嘉宏, 藤原宏志, 齋藤三郎
  • Journal Title: 数理解析研究所講究録 1618 Pages: 175-188
• [Journal Article] ラプラス変換の実逆変換への再生核空間の応用II (2008)
  • Author(s): 梶野直孝, 澤野嘉宏, 藤原宏志
  • Journal Title: 数理解析研究所講究録 1618 Pages: 189-191
• [Journal Article] New multiple-precision arithmetic environment and highaccurate numerical computations of ill-posed problems (2008)
  • Author(s): FUJIWARA, H.
  • Journal Title: Proceedings of the 4th JSIAM-SIMAI Seminar on Industrial and Applied Mathematics Vol.28 Pages: 21-29
• [Journal Article] 非適切問題を年頭においた多倍長精度並LU分解について (2008)
  • Author(s): 藤原宏志
  • Journal Title: 第57回理論応用力学講演会講演論文集 Pages: 521-522
• [Journal Article] Multiple-Precision Arithmetic,and its Application to High-Accurate Real Inversions of the Laplace Transform (2008)
  • Author(s): FUJIWARA, H.
  • Journal Title: Seminar Notes of Mathematical Science Vol.11 Pages: 51-63
• [Presentation] 多倍長計算環境下での数値Laplace逆変換の考察 (2011)
  • Author(s): 藤原宏志
  • Organizer: 第60回理論応用力学講演会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2011-03-08
• [Presentation] Remarks on Hosono's Method for the Complex Inverse Laplace Transform (2011)
  • Author(s): Hiroshi FUJIWARA
  • Organizer: The 1st SNU-Kyoto U Joint Seminar on Numerical Computation and Applied Analysis
  • Place of Presentation: Seoul National University, Seoul
  • Year and Date: 2011-02-21
• [Presentation] 多倍長計算による逆Laplace変換の数値的実現の試み (2011)
  • Author(s): 藤原宏志
  • Organizer: 応用数理学会 第14回環瀬戸内応用数理研究部会
  • Place of Presentation: 岡山理科大学(招待講演)
  • Year and Date: 2011-01-22
• [Presentation] 複素逆Laplace変換の数値計算における注意 (2010)
  • Author(s): 藤原宏志
  • Organizer: 日本計算数理工学シンポジウム2010
  • Place of Presentation: 新潟大学
  • Year and Date: 2010-12-10
• [Presentation] スペクトル法と多倍長計算による高精度数値計算 (2010)
  • Author(s): 藤原宏志
  • Organizer: 日本応用数理学会3部会連携「応用数理セミナー」
  • Place of Presentation: 国立情報学研究所
  • Year and Date: 2010-11-27
• [Presentation] Some remarks on numerical treatments of the Bromwich integral (2010)
  • Author(s): Hiroshi Fujiwara
  • Organizer: Taiwan-Japan Joint Workshop on Inverse Problem
  • Place of Presentation: National Taiwan University, Taipei
  • Year and Date: 2010-11-20
• [Presentation] 多倍長計算による非適切問題の大規模高精度計算の実現に向けて (2010)
  • Author(s): 藤原宏志
  • Organizer: オペレーションズリサーチ学会 研究部会「数理計画」第22回RAMPシンポジウム
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-10-29
• [Presentation] 多倍長区間精度による数値的に不安定な問題の取り扱い (2010)
  • Author(s): 藤原宏志
  • Organizer: 数理解析研究所 研究集会「科学技術計算アルゴリズムの数理的基盤と展開」
  • Place of Presentation: 数理解析研究所
  • Year and Date: 2010-10-19
• [Presentation] High-Accurate Computation of One-Loop Integrals by Several Hundred Digits Multiple-Precision Arithmetic (2010)
  • Author(s): FUJIWARA, Hiroshi
  • Organizer: 3rd Computational Particle Physics Workshop
  • Place of Presentation: KEK (High-Energy Accelerator Research Organization), Tsukuba.(Invited Talk)
  • Year and Date: 2010-09-24
• [Presentation] High-Accurate Computation of One-Loop Integrals by Several Hundred Digits Multiple-Precision Arithmetic (2010)
  • Author(s): FUJIWARA, Hiroshi
  • Organizer: 3rd Computational Particle Physics Workshop
  • Place of Presentation: 高エネルギー加速器研究機構(招待講演)
  • Year and Date: 2010-09-24
• [Presentation] 高精度科学技術計算のための多倍長計算環境の設計・実装と応用(日本数学会応用数学分科会・特別講演) (2010)
  • Author(s): 藤原宏志
  • Organizer: 日本数学会2010年度秋季総合分科
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-23
• [Presentation] 高精度科学技術計算のための多倍長計算環境の設計・実装と応用 (2010)
  • Author(s): 藤原宏志
  • Organizer: 日本数学会2010年度秋季総合分科 応用数学分科会
  • Place of Presentation: 名古屋大学(招待講演)
  • Year and Date: 2010-09-23
• [Presentation] Multiple-Precision Interval Arithmetic and their Applications (2010)
  • Author(s): Hiroshi Fujiwara
  • Organizer: The Third China-Japan-Korea Joint Conference on Numerical Mathematics
  • Place of Presentation: Gangneung-Wonju National University,Gangneung
  • Year and Date: 2010-08-20
• [Presentation] 実逆Laplace変換とBromwich積分との比較 (2010)
  • Author(s): 藤原宏志
  • Organizer: 第59回理論応用力学講演会
  • Place of Presentation: 日本学術会議
  • Year and Date: 2010-06-10
• [Presentation] MREに対する多倍長精度スペクトル法による3次元数値シミュレーション (2010)
  • Author(s): 藤原宏志
  • Organizer: 第59回理論応用力学講演会
  • Place of Presentation: 日本学術会議
  • Year and Date: 2010-06-09
• [Presentation] PC・クラスタ向きの多倍長計算環境の開発と科学技術計算への応用 (2010)
  • Author(s): 藤原宏志
  • Organizer: 第15回日本計算工学会
  • Place of Presentation: 九州大学
  • Year and Date: 2010-05-28
• [Presentation] Numerical Real Inversion of the Laplace Transform by Multiple-Precision Arithmetic (2010)
  • Author(s): Hiroshi Fujiwara
  • Organizer: AMS 2010 Spring Southeastern Sectional Meeting #1057
  • Place of Presentation: University of USA Kentucky, Lexington
  • Year and Date: 2010-03-28
• [Presentation] PC・クラスタ向きの多倍長計算環境の開発と科学技術計算での利用 (2010)
  • Author(s): 藤原宏志
  • Organizer: 天体力学N体力学研究会
  • Place of Presentation: 千葉大学
  • Year and Date: 2010-03-20
• [Presentation] Numerical Real Inversion of the Laplace Transform by Reproducing Kernel and Multiple-Precision Arithmetic (2009)
  • Author(s): FUJIWARA, Hiroshi
  • Organizer: 2009 Taiwan-Japan Joint workshop on Numerical Analysis and Scientific Computation
  • Place of Presentation: Nat.Taiwan University, Taipei
  • Year and Date: 2009-11-08
• [Presentation] Multiple-Precision Arithmetic and Real Inversion of the Laplace Transform (2009)
  • Author(s): FUJIWARA, Hiroshi
  • Organizer: International Workshop on Applied Mathematics and Computational Mathematics
  • Place of Presentation: 西安交通大学,西安
  • Year and Date: 2009-08-22
• [Presentation] Numerical Real Inversion of the Laplace Transform by Reproducing Kernel and Multiple-Precision Arithmetic (2009)
  • Author(s): FUJIWARA, Hiroshi
  • Organizer: 7th ISAAC Congress
  • Place of Presentation: Imperial College London, London.(Distinguished session talk)
  • Year and Date: 2009-07-15
• [Presentation] Numerical Real Inversion of the Laplace Transform by Reproducing Kernel and Multiple-Precision Arithmetic (2009)
  • Author(s): FUJIWARA, Hiroshi
  • Organizer: 7th ISAAC Congress
  • Place of Presentation: Imperial College, Londonイギリス
  • Year and Date: 2009-07-15
• [Presentation] 熱方程式の境界値逆問題の解の再構成について (2009)
  • Author(s): 藤原宏志、磯祐介
  • Organizer: 第58回理論応用力学講演会
  • Place of Presentation: 日本学術会議
  • Year and Date: 2009-06-11
• [Presentation] 数値的に不安定な線型問題のための多倍長精度・並列直接解法ライブラリの開発 (2008)
  • Author(s): 藤原宏志
  • Organizer: 日本計算数理工学会シンポジウム
  • Place of Presentation: 福井大学
  • Year and Date: 2008-11-28
• [Presentation] 再生核空間での正則化法に基く実逆ラフラス変の数値計算と実装 (2008)
  • Author(s): 藤原宏志
  • Organizer: 数値解析における理論・手法・応用
  • Place of Presentation: 数理解析研究所
  • Year and Date: 2008-11-13
• [Presentation] Numerical Real Inversion of the Laplace Transform (2008)
  • Author(s): FUJIWARA, H.
  • Organizer: Taiwan-Japan Joint Workshop on Inverse Problems
  • Place of Presentation: Academia Sinica, Taipei
  • Year and Date: 2008-11-01
• [Presentation] Multiple-Precision Arithmetic and its Application to Numerically Unstable Problems with Regularization Methods (2008)
  • Author(s): FUJIWARA, Hiroshi
  • Organizer: The International Conference on Inverse Problems and its Applications
  • Place of Presentation: Fudan University, Shanghai.(Invited Talk)
  • Year and Date: 2008-10-11
• [Presentation] Multiple-Pretision Arithmetic and its Application to Numerically Unstable Problems with Regularization (2008)
  • Author(s): FUJIWARA, H.
  • Organizer: The International Conference on Inverse Problems and its Applications
  • Place of Presentation: Fudan University, Shanghai
  • Year and Date: 2008-10-11
• [Presentation] 再生核空間上での実逆ラプラス変換とその計算機上での実現 (2008)
  • Author(s): 藤原宏志
  • Organizer: 再生核の応用についての研究
  • Place of Presentation: 数理解析研究所
  • Year and Date: 2008-09-12
• [Presentation] Multiple-preciSion parallel LU decomposition for numerically unstable problems (2008)
  • Author(s): FUJIWARA, H.
  • Organizer: The Second China-Japan-South. Korea Workshop on Numerical Mathematics
  • Place of Presentation: Weihai, China
  • Year and Date: 2008-08-26
• [Presentation] PCクラスタでの多倍長計算の実装と利用 (2008)
  • Author(s): 藤原宏右
  • Organizer: 先駆的科学計算に関するフォーラム
  • Place of Presentation: 九州大学
  • Year and Date: 2008-08-08
• [Presentation] 非適切問題を念頭においた多倍長精度並列LU分解について (2008)
  • Author(s): 藤原宏志
  • Organizer: 第57回理論応用力学講演会
  • Place of Presentation: 日本学術会議
  • Year and Date: 2008-06-12
• [Presentation] PC・WS用の多倍長計算環境の開発とその利用法 (2008)
  • Author(s): 藤原宏志
  • Organizer: 多倍長精度計算フォーラム
  • Place of Presentation: 工学院大学
  • Year and Date: 2008-02-23
• [Presentation] 多倍長計算による高精度数値的手法の実現 (2008)
  • Author(s): 藤原宏志
  • Organizer: 複素解析の発展とその応用
  • Place of Presentation: 桐生市市民文化会館
  • Year and Date: 2008-01-25
• [Remarks] ホームページ
  • URL: http://www-an.acs.i.kyoto-u.ac.jp/~fujiwara/exflib
• [Patent(Industrial Property Rights)] 逆ラプラス変換プログラム,逆ラプラス変換のためのテーブル作成プログラム,逆ラプラス変換の数値解算出プログラム,および逆ラプラス変換装置 (2008)
  • Inventor(s): 藤原宏志, 齋藤三郎, 松浦勉
  • Industrial Property Number: 2008-203384
  • Filing Date: 2008-08-12
  • Acquisition Date: 2008-08-06
• [Patent(Industrial Property Rights)] 逆ラプラス変換プログラム(等) (2008)
  • Inventor(s): 藤原宏志(京都大学)、齋藤三郎(群馬大学)、松浦勉(群馬大学)
  • Industrial Property Rights Holder: 藤原宏志(京都大学)、齋藤三郎(群馬大学)、松浦勉(群馬大学)
  • Filing Date: 2008-08-12
  • Overseas
• [Patent(Industrial Property Rights)] 逆ラプラス変換プログラム(等) (2008)
  • Inventor(s): 藤原宏志(京都大学)、齋藤三郎(群馬大学)、松浦勉(群馬大学)
  • Industrial Property Rights Holder: 藤原宏志(京都大学)、齋藤三郎(群馬大学)、松浦勉(群馬大学)
  • Industrial Property Number: 2008-203384
  • Filing Date: 2008-08-06