Study of an approximated distribution using the continuous Euler transformation

• Project/Area Number: 19560067
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: Kyoto University
• Principal Investigator: OOURA Takuya Kyoto University, 数理解析研究所, 助教 (50324710)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 連続オイラー変換 / 超関数 / 近似 / 数値積分法 / 近似超関数 / 二重指数関数型数値積分 / Sinc近似 / IMT公式

Research Abstract

We show that the distributions are easily approximated by continuous functions using the continuous Euler transformation, and the linear map of the approximated distribution is high precision. The approximated distribution can be applied to the computation of numerical indefinite integration, two-dimensional oscillatory integration and a certain differential equation.

Research Products

• [Journal Article] Particle trajectories around a running cylinder or a sphere (2010)
  • Author(s): M. Shoji, H. Okamoto, T. Ooura
  • Journal Title: Fluid Dynamics Research 42 Pages: 25506-25506
  • NAID: 10028205798
  • Peer Reviewed
• [Journal Article] Particle trajectories around a running cylinder or a sphere (2010)
  • Author(s): M.Shoji, H.Okamoto, T.Ooura
  • Journal Title: Fluid Dynamics Research 42
  • NAID: 10028205798
  • Peer Reviewed
• [Journal Article] 連続オイラー変換による超関数の直接計算 (2009)
  • Author(s): 大浦拓哉
  • Journal Title: 数学 61(3) Pages: 93-306
  • NAID: 10026415315
  • Peer Reviewed
• [Journal Article] 二重指数関数型変換を用いた様々な積分変換の計算法 (2009)
  • Author(s): 大浦拓哉
  • Journal Title: 日本応用数理学会論文誌 Vol.19、No.1 Pages: 73-79
  • Peer Reviewed
• [Journal Article] 二重指数関数型変換を用いた様々な積分変換の計算法 (2009)
  • Author(s): 大浦拓哉
  • Journal Title: 日本応用数理学会論文誌 19 Pages: 73-79
  • Peer Reviewed
• [Journal Article] An IMT-type quadrature formula with the same asymptotic performance as the DE formula (2008)
  • Author(s): T. Ooura
  • Journal Title: J. Comput. Appl. Math 213 Pages: 232-239
  • Peer Reviewed
• [Journal Article] An IMT-type quadrature formula with the same asymptotic performance as the DE formula (2008)
  • Author(s): T. Ooura
  • Journal Title: J. Comput. Appl. Math. 213 Pages: 232-239
  • Peer Reviewed
• [Presentation] 戸田積分のDE公式による超高精度計算 (2009)
  • Author(s): 大浦拓哉
  • Organizer: 第38回数値解析シンポジウム(日本応用数理学会主催)
  • Place of Presentation: 静岡県熱川ハイツ
  • Year and Date: 2009-06-16
• [Presentation] 戸田積分のDE公式による超高精度計算 (2009)
  • Author(s): 大浦拓哉
  • Organizer: 第38回数値解析シンポジウム(日本応用数理学会主催)
  • Place of Presentation: 熱川ハイツ(静岡県)
  • Year and Date: 2009-06-16
• [Presentation] 連続オイラー変換による超関数の直接計算 (2007)
  • Author(s): 大浦拓哉
  • Organizer: 日本数学会2007年度秋季総合分科会「応用数学スペシャルセッション」
  • Place of Presentation: 東北大学
  • Year and Date: 2007-09-23
• [Remarks]
  • URL: http://www.kurims.kyoto-u.ac.jp/~ooura/profile-j.html
• [Remarks]
  • URL: http://www.kurims.kyoto-u.ac.jp/~ooura/profile-j.html
• [Remarks]
  • URL: http://www.kurims.kyoto-u.ac.ip/~ooura/index-i.html
• [Remarks]
  • URL: http://www.kurims.kyoto-u.ac.jp/~ooura/index-j.html