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Applications of the theory of reproducing kernels to the Tikhonov regularization

Research Project

Project/Area Number 19540164
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionGunma University

Principal Investigator

SAITOH Saburou  Gunma University, 大学院・工学研究科, 教授 (10110397)

Co-Investigator(Kenkyū-buntansha) MATSUURA Tsutomu  群馬大学, 大学院・工学研究科, 准教授 (80181692)
Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2007: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Keywords再生核の理論 / 再生核 / チホノフ正則化法 / 数値解析 / 計算機 / ラプラス変換 / 非線形連立方程式 / ステムの同定と逆 / チホノブ正則化法 / システムの同定 / 逆問題 / 数値実験 / 非線形解析 / 非線形システム / 連立非線形方程式
Research Abstract

再生核の理論をチホノフ正則化法に適用して、相当一般的なヒルベルト空間上の作用素方程式の数値解析的な解法を確立して、典型的な例として難問として有名なラプラス実逆変換の数値解析的解法に藤原宏志氏などと成功して、国内及び国際特許の申請を済ませるまで研究を進める事が出来た。他方、山田正人氏などと非線形システムの同定と逆を確立する新しい数学的な理論をある程度構成することに成功した。

Report

(3 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • Research Products

    (45 results)

All 2008 2007 Other

All Journal Article (22 results) (of which Peer Reviewed: 22 results) Presentation (16 results) Remarks (3 results) Patent(Industrial Property Rights) (4 results) (of which Overseas: 2 results)

  • [Journal Article] Real inversion formulas of the Laplace transform on weighted function spaces2008

    • Author(s)
      Sawano Yosihiro : Fujiwara Hiroshi ; Saitoh, Saburou
    • Journal Title

      Complex Anal. Oper. Theory 2 no. 3

      Pages: 511-521

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Theory of reproducing kernels---Applications to approximate solutions of bounded linear operator equations on Hilbert spaces2008

    • Author(s)
      Saitoh, Saburou
    • Journal Title

      (Japanese) Sugaku 60 no.3

      Pages: 248-271

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Identifications of non-linear systems.2008

    • Author(s)
      Yamada, Masato ; Saitoh, Saburou
    • Journal Title

      J.Comput. Math. Optim. 4 no. 1

      Pages: 47-60

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Real inversion of the Laplace transform in numerical singular value decomposition2008

    • Author(s)
      Fujiwara, Hiroshi ; Matsuura, Tsutomu, Saitoh, Saburou. Sawano Yosihiro
    • Journal Title

      J. Anal. Appl. 6 no. 1

      Pages: 55-68

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Real inversion formulas of the Laplace transform weighted function spaces2008

    • Author(s)
      Saitoh, Saburou
    • Journal Title

      Complex Ana1. Oper. Theory 2

      Pages: 511-521

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Theory of reproducing kernels---Applications to approximate solutions of bounded linear operator equations on Hilbert spaces. (Japanese)2008

    • Author(s)
      Saitoh, Saburou
    • Journal Title

      Sugaku 60

      Pages: 248-271

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Identifications of non-1inear systems2008

    • Author(s)
      Yamada, Masato
    • Journal Title

      J. Comput. Math. Optim. 4

      Pages: 47-60

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Real inversion of the Laplace transform in merical singular value decomposition2008

    • Author(s)
      Fujiwara, Hiroshi
    • Journal Title

      J. Anal. Appl. 6

      Pages: 55-68

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Identification of non-1inear systems2008

    • Author(s)
      M. Yamada
    • Journal Title

      Journal of Computational Mathematics and Optimization 4

      Pages: 47-60

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Real inversion of the Laplace transfgrm in numerical singular value decomposition2008

    • Author(s)
      H. Fujiwara
    • Journal Title

      Joumal of Analysis and Applications 6

      Pages: 55-68

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical real inversion formulas of the Laplace transform by using the sinc functions2007

    • Author(s)
      Matsuura, Tsutomu ; Al-Shuaibi, A. ; Fujiwara, Hiroshi ; Saitoh, Saburou ; Sugihara, Masaaki
    • Journal Title

      Far East J. Math. Sci. (FJMS) 27 no. 1

      Pages: 1-14

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tikhonov regularization and the theory of reproducing kernels2007

    • Author(s)
      Saitoh, Saburou
    • Journal Title

      Cubo 9 no. 3

      Pages: 65-74

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analytical and numerical solutions of linear singular integral equations2007

    • Author(s)
      Itou, Hiroshi ; Saitoh, Saburou
    • Journal Title

      Int. J. Appl. Math. Stat. 12 No. D07

      Pages: 76-89

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Representations of inverse functions by the integral transform with the sign kernel2007

    • Author(s)
      Yamada Masato ; Matsuura, Tsutomu ; Saitoh, Saburou
    • Journal Title

      Fract. Calc. Appl. Anal. 10 no. 2

      Pages: 161-168

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical real inversion formulas of the Laplace transform by using a Fredholm integral equation of the second kind2007

    • Author(s)
      Matsuura, Tsutomu ; Al-Shuaibi, A. ; Fujiwara, Hiroshi ; Saitoh, Saburou
    • Journal Title

      J. Anal. Appl. 5 no. 2

      Pages: 123-136

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analytical and numerical solutions of the inhomogeneous heat equation2007

    • Author(s)
      Matsuura, Tsutomu ; Saitoh, Saburou
    • Journal Title

      J. Concr. Appl. Math. 5 no. 3

      Pages: 237-254

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Representations of inverse fumctions by the integral transform with the sign function2007

    • Author(s)
      M. Yamada
    • Journal Title

      Fractional Calculus & Applied Analysis 10

      Pages: 161-168

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical real inversion formUlas of the Laplace transfbrm by using a Fredholm integral equation of the second kind2007

    • Author(s)
      T. Matsuura
    • Journal Title

      Joumal of Analysis and Applications 5

      Pages: 123-136

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analytical and numerical solutions of the inhomogeneous heat equation2007

    • Author(s)
      T. Matsuura
    • Journal Title

      j. Concr. Appl. Math. 5

      Pages: 237-254

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Applications of Tikhonov regularization to inverse problems using reproducing kemels2007

    • Author(s)
      S. Saitoh
    • Journal Title

      Jdumal of Physics:Conference Series 73

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analytical and numerical solutions of linear sungular integral equations2007

    • Author(s)
      H. Itoh
    • Journal Title

      International J. of APplied Math.& Statistics 12

      Pages: 76-89

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical real inversion formulas of the Laplace transform by using a Fredholm integral equation of the second kind2007

    • Author(s)
      T. Matsuura
    • Journal Title

      Journal of Analysis and Applications 5

      Pages: 123-136

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] 連立非線形方程式の解の具体的な表現について2008

    • Author(s)
      山田正人, 齋藤三郎
    • Organizer
      日本数学会2008年度秋季総合分科会
    • Place of Presentation
      東京
    • Year and Date
      2008-09-26
    • Related Report
      2008 Final Research Report
  • [Presentation] 非線形写像の逆写像の積分表現2008

    • Author(s)
      山田正人, 齋藤三郎
    • Organizer
      日本応用数理学会2008年度年会
    • Place of Presentation
      東京
    • Year and Date
      2008-09-26
    • Related Report
      2008 Final Research Report
  • [Presentation] 連立非線形方程式の解の具体的な表現について2008

    • Author(s)
      齋藤三郎
    • Organizer
      日本数学会
    • Place of Presentation
      東京
    • Year and Date
      2008-09-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] Singular integrals and natural regularizations2008

    • Author(s)
      澤野嘉宏
    • Organizer
      日本数学会
    • Place of Presentation
      東京
    • Year and Date
      2008-09-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] Identification of non-linear systems2008

    • Author(s)
      齋藤三郎, 山田正人
    • Organizer
      日本数学会2008 年度年会
    • Place of Presentation
      大阪
    • Year and Date
      2008-03-26
    • Related Report
      2008 Final Research Report
  • [Presentation] 非線形システムの逆について2008

    • Author(s)
      齋藤三郎, 山田正人
    • Organizer
      日本数学会2008年度年会
    • Place of Presentation
      大阪
    • Year and Date
      2008-03-26
    • Related Report
      2008 Final Research Report
  • [Presentation] 荷重付L^2関数空間のラプラス変換のコンパクト性2008

    • Author(s)
      澤野 嘉宏
    • Organizer
      日本数学会
    • Place of Presentation
      近畿大
    • Year and Date
      2008-03-26
    • Related Report
      2007 Annual Research Report
  • [Presentation] Identifications of non-linear systems2008

    • Author(s)
      齋藤 三郎
    • Organizer
      日本数学会
    • Place of Presentation
      近畿大
    • Year and Date
      2008-03-26
    • Related Report
      2007 Annual Research Report
  • [Presentation] 菲線形システムの逆について2008

    • Author(s)
      齋藤 三郎
    • Organizer
      日本数学会
    • Place of Presentation
      近畿大
    • Year and Date
      2008-03-26
    • Related Report
      2007 Annual Research Report
  • [Presentation] ラプラス変換の実逆変換の困難性と克服について2007

    • Author(s)
      齋藤三郎, 藤原宏志
    • Organizer
      日本数学会
    • Place of Presentation
      東北大
    • Year and Date
      2007-09-23
    • Related Report
      2008 Final Research Report
  • [Presentation] ラプラス変換の実逆変換の困難と克服について2007

    • Author(s)
      齋藤 三郎
    • Organizer
      日本数学会
    • Place of Presentation
      東北大
    • Year and Date
      2007-09-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Practical inversion formulas for linear systems2007

    • Author(s)
      齋藤三郎, 山田正人
    • Organizer
      ISAAC Ankara Congress
    • Place of Presentation
      アンカラ、トルコ
    • Year and Date
      2007-08-15
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Applications of reproducing kernels to numerical analysis through the Tikhonov regularization2007

    • Author(s)
      齋藤三郎
    • Organizer
      SEAMS-GMU International Conference
    • Place of Presentation
      インドネシア、Yogyakarta
    • Year and Date
      2007-07-25
    • Related Report
      2008 Final Research Report
  • [Presentation] Applications of reproducing kernels to numerical analysis through the tikhonov regularization2007

    • Author(s)
      齋藤 三郎
    • Organizer
      SEAMS-GMU Intemational Conference
    • Place of Presentation
      インドネシア、Yogyakarta
    • Year and Date
      2007-07-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley-Wiener spaces2007

    • Author(s)
      齋藤三郎
    • Organizer
      Third International Conference on Computational and Harmonic Analysis
    • Place of Presentation
      上海、中国
    • Year and Date
      2007-06-21
    • Related Report
      2008 Final Research Report
  • [Presentation] Analytical and numerical inversion formulas in the Gaussian convoluti on by using the Paley-Wiener spaces2007

    • Author(s)
      齋藤 三郎
    • Organizer
      Third Intemational Conference on Computational and Harmonic Analysis
    • Place of Presentation
      上海、中国
    • Year and Date
      2007-06-21
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

      https://univ-db.media.gunma-u.ac.jp/public/main.php?gakubu=31000&gakka=31800&kouza=31830&q=&btnS=%E6%A4%9C%E7%B4%A2&pid=res_search_list

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      https://univ-db.media.gunnia-u.ac.jp/public/main.php?gakubu=31000&gakka=31800&kouza=31830&q=&btnS=%E6%A4%9C%E7%B4%A2&pid=res_search_list

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      https://univ-db.medis.gunma-u.ac.jp/public/main.php~gakubu=31000&gakka=31800&kouza=31830&q=&btnS=%E6%A4%9C%E7%B4%A2%&pid=res_search_list

    • Related Report
      2007 Annual Research Report
  • [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 Rights Holder
      国立大学法人群馬大学、国立大学法人京都大学
    • Filing Date
      2008-08-12
    • Related Report
      2008 Final Research Report
    • Overseas
  • [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 Rights Holder
      国立大学法人群馬大学、国立大学法人京都大学
    • Filing Date
      2008-08-12
    • Related Report
      2008 Annual Research Report
    • Overseas
  • [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ラグラム、逆ラプラス変換の数値算出プログラム、および逆ラプラス変換装置2007

    • Inventor(s)
      藤原宏志、齋藤三郎、松浦勉
    • Industrial Property Rights Holder
      国立大学法人群馬大学、国立大学法人京都大学
    • Industrial Property Number
      2007-210946
    • Filing Date
      2007-08-13
    • Related Report
      2008 Final Research Report
  • [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ラグラム、逆ラプラス変換の数値算出プログラム、および逆ラプラス変換装置2007

    • Inventor(s)
      藤原 宏志
    • Industrial Property Rights Holder
      京都大学と群馬大学
    • Filing Date
      2007-08-13
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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