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Applications of the reproducing kernel theory to inverse problems and their engineering approach

Research Project

Project/Area Number 20540105
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionGunma University

Principal Investigator

MATSUURA Tsutomu  Gunma University, 大学院・工学研究科, 准教授 (80181692)

Co-Investigator(Kenkyū-buntansha) SAITOH Saburou  群馬大学, 名誉教授 (10110397)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords逆問題 / 再生核理論 / ラプラス実逆変換 / 正則化
Research Abstract

We developed a new type of Thihonov regularization combined with the theory of reproducing kernels. Using our method of regularization we have challenged some famous and historically difficult inverse problems. Furthermore we designed concrete algorithms for solving those problems. In particular we studied real inversion of Laplace transform, solving method by singular value decomposition, representation of inverse transform of nonlinear mapping and separation of mixed signals. In addition for engineer in the field we filed a patent application of our algorithm for inversion of Laplace transform.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (39 results)

All 2011 2010 2009 2008

All Journal Article (21 results) (of which Peer Reviewed: 18 results) Presentation (14 results) Patent(Industrial Property Rights) (4 results) (of which Overseas: 3 results)

  • [Journal Article] Approximate solutions for the Poisson equation by using the theory of reproducing kernels2011

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

      Journal of the Japan Society of Applied Electromagnetics and Mechanics (in press.)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Separation and reproduction of mixed images using 2-D complex wavelet transform2010

    • Author(s)
      Tsutomu Matsuura, Amirul Faiz, Kouji Kiryu
    • Journal Title

      Applied Mechanics and Materials Vol.36

      Pages: 466-475

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Integral and Direct Representations of Nonlinear Inverse Mapping2010

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

      Applied Mechanics and Materials Vol.36

      Pages: 476-484

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A numerical construction of a natural inverse of any matrix by using the theory of reproducing kernels with the Tikhonov regularization2010

    • Author(s)
      K.Iwamura, T.Matsuura, S.Saitoh
    • Journal Title

      Far East Journal of Mathematical Education Vol.4

      Pages: 141-149

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Source inversion of heat conduction from a finite number of observation data2010

    • Author(s)
      L.Castro, Q.Chen, S.Saitoh
    • Journal Title

      Appl.Anal. Vol.89

      Pages: 801-813

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Singular integral inequalities and natural regularizations2010

    • Author(s)
      Y.Sawano, M.Yamada, S.Saitoh
    • Journal Title

      Math.Inequal.Appl. Vol.13

      Pages: 289-303

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Real inversion for mulas and numerical experiments of the Laplace transform by using the theory of reproducing kernels2010

    • Author(s)
      Tsutomu Matsuura
    • Journal Title

      Procedia Social and Behavioral Sciences Vol.2

      Pages: 111-119

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Separation and reproduction of mixed images using 2-D complex wavelet transform2010

    • Author(s)
      Tsutomu Matsuura, Amirul Faiz, Kouji Kiryu
    • Journal Title

      Applied Mechanics and Materials

      Volume: 36 Pages: 466-475

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integral and Direct Representations of Nonlinear Inverse Mapping2010

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

      Applied Mechanics and Materials

      Volume: 36 Pages: 476-484

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A numerical construction of a natural inverse of any matrix by using the theory of reproducing kernels with the Tikhonov regularization2010

    • Author(s)
      K.Iwamura, T.Matsuura, S.Saitoh
    • Journal Title

      Far.East Journal of Mathematical Education

      Volume: 4 Pages: 141-149

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Source inversion of heat conduction from a finite number of observation data2010

    • Author(s)
      L.Castro, Q.Chen, S.Saitoh
    • Journal Title

      Appl.Anal.

      Volume: 89 Pages: 801-813

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singular integral inequalities and natural regularizations2010

    • Author(s)
      Y.Sawano, M.Yamada, S.S aitoh
    • Journal Title

      Math.Inequal.Appl.

      Volume: 13 Pages: 289-303

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Real inversion formulas and numerical experiments of the Laplace transform by using the theory of reproducing kernels2010

    • Author(s)
      Tsutomu Matsuura
    • Journal Title

      Procedia Social and Behavioral Sciences 2

      Pages: 111-119

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical Real Inversion of the Laplace Transform by using a high-acuuracy numerical method2009

    • Author(s)
      H.Fujiwara, T.Matsuura, S.Saitoh, Y.Sawano
    • Journal Title

      Further Progress in Analysis(World Scientific)

      Pages: 574-585

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analytical and numerical real inversion formulas of the Laplace transform2009

    • Author(s)
      T.Matsuura, S.Saitoh
    • Journal Title

      More Progresses in Analysis(World Scientific)

      Pages: 191-200

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical Cauchy problems for the Laplace equation2009

    • Author(s)
      T.Matsuura, S.Saitoh, M.Yamamoto
    • Journal Title

      More Progresses in Analysis(World Scientific)

      Pages: 1375-1384

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article]2009

    • Author(s)
      H.Fujiwara
    • Journal Title

      Further Progress in Analysis(World Scientific)

      Pages: 574-585

    • Related Report
      2009 Annual Research Report
  • [Journal Article]2009

    • Author(s)
      T.Matsuura
    • Journal Title

      More Progresses In Analysis(World Scientific)

      Pages: 191-200

    • Related Report
      2009 Annual Research Report
  • [Journal Article]2009

    • Author(s)
      T.Matsuura
    • Journal Title

      More Progresses In Analysis(World Scientific)

      Pages: 1375-1384

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Real Inversion of the Laplace Transform in Numerical Singular Value Decomposition2008

    • Author(s)
      H.Fujiwara, T.Matsuura, S.Saitoh, Y. Sawano
    • Journal Title

      Journal of Analysis and Applications Vol.6

      Pages: 55-68

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Real Inversion of the Laplace Transform in Numerical Si ngular Value Decomposition2008

    • Author(s)
      H. Fujiwara
    • Journal Title

      Journal of Analysis and Applications 6

      Pages: 55-56

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Approximate solutions for the Poisson equation by using the theory of reproducing kernels2010

    • Author(s)
      松浦勉
    • Organizer
      Asia-Pacific Symposium on Applied Electromagnetics and Mechanics
    • Place of Presentation
      Hotel Istana Kuala Lumpur(クアラルンプール、マレーシア)
    • Year and Date
      2010-07-29
    • Related Report
      2010 Final Research Report
  • [Presentation] Approximate solutions for the Poisson equation by using the theory of reproducing kernels.2010

    • Author(s)
      松浦勉
    • Organizer
      Asia-Pacific Symposium on Applied Electromagnetics and Mechanics
    • Place of Presentation
      マレーシア,クアラルンプール
    • Year and Date
      2010-07-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Integral and Direct Representations of Nonlinear Inverse Mapping2010

    • Author(s)
      松浦勉
    • Organizer
      CPIM 2010
    • Place of Presentation
      桐生市民文化会館(群馬県)
    • Year and Date
      2010-03-18
    • Related Report
      2010 Final Research Report
  • [Presentation] Integral and Direct Representations of Nonlinear Inverse Mapping2010

    • Author(s)
      Tsutomu Matsuura
    • Organizer
      CPIM 2010
    • Place of Presentation
      Kiryu, Japan
    • Year and Date
      2010-03-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] Real inversion formulas and its numerical experiments of the Laplace transform by using the theory of reproducing kernels2009

    • Author(s)
      松浦勉
    • Organizer
      SPC 2009
    • Place of Presentation
      桐生市市民文化会館(群馬県)
    • Year and Date
      2009-10-29
    • Related Report
      2010 Final Research Report
  • [Presentation] Real inversion formulas and its numerical experiments of the Laplace transform by using the theory of reproducing kernels2009

    • Author(s)
      Tsutomu Matsuura
    • Organizer
      SPC 2009
    • Place of Presentation
      Kiryu, Japan
    • Year and Date
      2009-10-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] 非線形写像の逆写像の積分表現2009

    • Author(s)
      松浦勉
    • Organizer
      日本機械学会関東支部ブロック合同講演会2009 前橋
    • Place of Presentation
      群馬高専(群馬県)
    • Year and Date
      2009-09-26
    • Related Report
      2010 Final Research Report
  • [Presentation] 非線形写像の逆写像の積分表現2009

    • Author(s)
      松浦勉
    • Organizer
      日本機械学会関東支部ブロック合同講演会2009前橋
    • Place of Presentation
      群馬高専
    • Year and Date
      2009-09-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Numerical solutions of nonlinear simultaneous equations2009

    • Author(s)
      Tsutomu Matsuura
    • Organizer
      ISAAC 2009
    • Place of Presentation
      Imperial College London
    • Year and Date
      2009-07-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] Numerical solutions of nonlinear simultaneous equations2009

    • Author(s)
      松浦勉
    • Organizer
      ISAAC 2009
    • Place of Presentation
      Imperial College London(ロンドン、英国)
    • Year and Date
      2009-07-11
    • Related Report
      2010 Final Research Report
  • [Presentation] 再生核理論を用いたラプラス実逆変換2008

    • Author(s)
      松浦勉
    • Organizer
      日本機械学会関東支部ブロック合同講演会
    • Place of Presentation
      小山高専(栃木県)
    • Year and Date
      2008-09-19
    • Related Report
      2010 Final Research Report
  • [Presentation] sinc関数近似によるラプラス実逆変換アルゴリズム2008

    • Author(s)
      松浦勉
    • Organizer
      日本機械学会関東支部ブロック合同講演会
    • Place of Presentation
      小山高専(栃木県)
    • Year and Date
      2008-09-19
    • Related Report
      2010 Final Research Report
  • [Presentation] 再生核理論を用いたラプラス実逆変換2008

    • Author(s)
      松浦勉
    • Organizer
      日本機械学会関東支部ブロック合同講演会
    • Place of Presentation
      小山高専
    • Year and Date
      2008-09-19
    • Related Report
      2008 Annual Research Report
  • [Presentation] sinc関数近似によるラプラス実逆変換アルゴリズム2008

    • Author(s)
      松浦勉
    • Organizer
      日本機械学会関東支部ブロック合同講演会
    • Place of Presentation
      小山高専
    • Year and Date
      2008-09-19
    • Related Report
      2008 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2010

    • 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
      2010-02-16
    • Related Report
      2010 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2010

    • 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
      2010-02-16
    • Related Report
      2009 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2009

    • 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
      2009-08-12
    • Related Report
      2010 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

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Published: 2008-04-01   Modified: 2025-11-18  

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