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Research of the applications of the theory of reproducing kernels

Research Project

Project/Area Number 16540137
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, Department of Mathematics, Faculty of Engineering, Professor, 工学部, 教授 (10110397)

Co-Investigator(Kenkyū-buntansha) IKEHATA Masaru  GUNMA UNIVERSITY, Department of Mathematics, Faculty of Engineering, Professor, 工学部, 教授 (90202910)
AMANO Kazuo  GUNMA UNIVERSITY, Department of Mathematics, Faculty of Engineering, Professor, 工学部, 助教授 (90137795)
TNUMA Kazumi  GUNMA UNIVERSITY, Department of Mathematics, Faculty of Engineering, Associated Professor, 工学部, 助教授 (60217156)
AMOU Masaaki  GUNMA UNIVERSITY, Department of Mathematics, Faculty of Engineering, Associated Professor, 工学部, 助教授 (60201901)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2004: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsReproducing kernels / Tikhonov regularization / Numerical Analysis / Algorithm / Computer / Computer Graphic / Analysis / Applicable Analysis / 近似解法 / 再生核 / チィコノフ正則化法 / 離散化
Research Abstract

We established a general theory of the applications of the theory of reproducing kernels to the Tikhonov regularization and derived many concrete results in inverse problems as applications of the general theory. typical results are the effective inversion formulas for the heat conduction and the real inversion formula of the Laplace transform that are very famous ill-posed problems and are well-known as very difficult problems. We succeeded in their numerical analysis and showed the results in the computer graphics with our related collaborators-in particular, Professors Tsutomu Matuura and Hiroshi Fujiwara. Furthermore, we were able to publish their results in which are major international journals. We derived the concrete results in ordinary differential equations, the wave equation, Poisson equation, Dirichlet problem, and so on.

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (56 results)

All 2007 2006 2005 2004 Other

All Journal Article (56 results)

  • [Journal Article] Analytical and numerical solutions of the Inhomogeneous heat equation2007

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

      Journal of concrete and applicable mathematics 5・3

      Pages: 237-257

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Analytical and numerical solutions of the Inhomogeneous heat equation2007

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

      Journal of concrete and applicable mathematics 5. no.3

      Pages: 237-257

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Analytica and numerical solutions of the inhomogeneous heat equation2007

    • Author(s)
      T.Matsuura
    • Journal Title

      Journal of concrete and applicable mathematics 5・3

      Pages: 237-254

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley-Wiener spaces2006

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

      Applicable Analysis 85・8

      Pages: 901-915

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley-Wiener spaces2006

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

      Applicable Analysis 85, No.8

      Pages: 901-915

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley-Wiener spaces2006

    • Author(s)
      T.Matsuura
    • Journal Title

      Applicable Analysis 85・8

      Pages: 901-915

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Applications of the Tikhonov regularization and reproducing kernels. Mathematical sciences of fracture phenomena.2005

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

      Sem. Math. Sci. 34

      Pages: 27-46

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Approximate and analytical inversion formulas in heat conduction on multidimensional spaces. Inverse problems : modeling and simulation.2005

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

      J. Inverse Ill-Posed Probl. 13・3-6

      Pages: 479-493

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Application of reproducing kernels to best approximations, Tikhonov regularizations and inverse problems.2005

    • Author(s)
      S.Saitoh
    • Journal Title

      Advances in analysis

      Pages: 439-445

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Constructions of approximate solutions for linear differential equations by reproducing kernels and inverse problems.2005

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

      Advances in analysis

      Pages: 335-343

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Operator equations and best approximation problems in reproducing kernel Hilbert spaces with Tikhonov regularization2005

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

      Advances in analysis

      Pages: 99-107

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Theory of functions2005

    • Author(s)
      Saitoh, Saburoh
    • Journal Title

      Sci. Math. Jpn. 62・2

      Pages: 195-197

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Dirichlet principle using computers.2005

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

      Appl. Anal. 84・10

      Pages: 989-1003

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Best approximation, Tikhonov regularization and reproducing kernels.2005

    • Author(s)
      Saitoh, Saburoh
    • Journal Title

      Kodai Math. J. 28・2

      Pages: 359-367

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Numerical inversion formulas in the wave equation.2005

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

      J. Comput. Math. Optim. 1・1

      Pages: 1-19

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Analytical and numerical solutions of linear ordinary differential equations with constant coefficients.2005

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

      J. Anal. Appl. 3・1

      Pages: 1-17

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Applications of the Tikhonov regularization and reproducing kernels. Mathematical sciences of fracture phenomena.2005

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

      Sem. Math. Sci. 34

      Pages: 27-46

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Approximate and analytical inversion formulas in heat conduction on multidimensional spaces. Inverse problems : modeling and simulation.2005

    • Author(s)
      Matuura, T., Saitoh, S., Trong, D.D.
    • Journal Title

      J. Inverse III-Posed Probl. 13, no.3-6

      Pages: 479-493

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Application of reproducing kernels to best approximations. Tikhonov regularizations and inverse problems.2005

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

      Advances in analysis

      Pages: 439-445

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Constructions of approximate solutions for linear differential equations by reproducing kernels and inverse problems.2005

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

      Advances in analysis

      Pages: 335-343

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Operator equations and best approximation problems in reproducing kernel Hilbert spaces with Tikhonov regularization2005

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

      Advances in analysis

      Pages: 99-107

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Theory of functions2005

    • Author(s)
      Saitoh, Saburoh
    • Journal Title

      Sci. Math. Jpn. 62, no.2

      Pages: 195-197

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Dirichlet principle using computers2005

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

      Appl. Anal. 84, no.10

      Pages: 989-1003

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Bestapproximation, Tikhonov regularization and reproducing kernels.2005

    • Author(s)
      Saitoh Saburoh
    • Journal Title

      Kodai Math. J. 28, no.2

      Pages: 359-367

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Numerical inversion formulas in the wave equation.2005

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

      J. Comput. Math. Optim. 1, no.1

      Pages: 1-19

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Analytical and numerical solution of linear ordinary differential equations with constant coefficients.2005

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

      J. Anal. Appl. 3, no.1

      Pages: 1-17

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Best approximation, Tikhonov regularization and reproducing kernels2005

    • Author(s)
      S.Saitoh
    • Journal Title

      Kodai Math.J. 28,2

      Pages: 359-367

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Dirichlet principle using computers2005

    • Author(s)
      T.Matsuura
    • Journal Title

      Applicable Analysis 84,10

      Pages: 989-1003

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Operator equations and best approximation problems in reproducing kernel Hilbert spaces with Tikhonov regularization2005

    • Author(s)
      S.Saitoh
    • Journal Title

      Advaces in analysis

      Pages: 99-107

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Constructions of approximate solutions for linear differential equations by reproducing kernels and inverse problems2005

    • Author(s)
      M.Asaduzzaman
    • Journal Title

      Advances in analysis

      Pages: 335-343

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Applications of reproducing kernels to best approximations, Tikhonov regularizations and inverse problems2005

    • Author(s)
      S.Saitoh
    • Journal Title

      Advances in analysis

      Pages: 439-445

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Approximate and analytical inversion formulas in heat conduction in multidimensional spaces2005

    • Author(s)
      T.Matsuura
    • Journal Title

      Journal of Inverse and III-Posed Problems 13,3-6

      Pages: 479-493

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Numerical inversion formulas in the wave equation2005

    • Author(s)
      T.Matsuura
    • Journal Title

      Journal of Computational Mathematics and Optimization 1・1

      Pages: 1-19

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Analytical and numerical solutions of linear ordinary differential equations with constant coefficients2005

    • Author(s)
      T.Matsuura
    • Journal Title

      Journal of Analysis and Applications 3・1

      Pages: 1-17

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A method by separation of variables for the second order ordinary differential equations2005

    • Author(s)
      T.Tada
    • Journal Title

      Journal of Computational Mathematics and Optimization 3・2

      Pages: 289-296

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A method by separation of variables for the second order ordinary differential equations.2004

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

      Int. J Math. Sc. 3・2

      Pages: 285-292

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A method by transforms of variables for the first order nonlinear ordinary differential equations.2004

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

      Far East J. Math. Sci. (FJMS) 14・3

      Pages: 393-403

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Numerical solutions of the Poisson equation.2004

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

      Appl. Anal. 83・10

      Pages: 1037-1051

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Analytical and numerical solutions of the inhomogeneous wave equation.2004

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

      Aust. J. Math. Anal. Appl. 1・1

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Approximate real inversion formulas of the Gaussian convolution.2004

    • Author(s)
      S.Saitoh
    • Journal Title

      Anal. Appl. 83・7

      Pages: 727-733

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A method by separation of variables for the first order nonlinear ordinary differential equations.2004

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

      J. Anal. Appl. 2・1

      Pages: 51-63

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A method by separation of variables for the second ordinary differential equations.2004

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

      Int. J. Math. Sc. 3, no.2

      Pages: 285-292

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A method by transforms of variables for the first order nonlinear ordinary differential equations.2004

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

      Far East J. Math. Sci. (FJMS) 14, no.3

      Pages: 393-403

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Numerical solutions of the Poisson equation.2004

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

      Appl. Anal. 83, no.10

      Pages: 1037-1051

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Analytical and numerical solutions of the inhomogeneous wave equation.2004

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

      Aust. J. Math. Anal. Appl. 1, no.2

      Pages: 7-18

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Approximate real inversion formulas of the Gaussian convolution.2004

    • Author(s)
      Tada, T.
    • Journal Title

      Anal. Appl. 83

      Pages: 727-733

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A method by separation of variables for the first order nonlinear ordinary differential equations.2004

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

      J. Anal. Appl. 2, no.1

      Pages: 51-63

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A method by separation of variables for the first order nonlinear ordinary differential equations2004

    • Author(s)
      T.Tada
    • Journal Title

      Journal of Analysis and Applications 2・1

      Pages: 51-63

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Approximate real inversion formulas of the Gaussian convolution2004

    • Author(s)
      S.Saitoh
    • Journal Title

      Applicable Analysis 83・7

      Pages: 727-733

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Numerical solutions of the Poisson equation2004

    • Author(s)
      T.Matsuura
    • Journal Title

      Applicable Analysis 83・10

      Pages: 1037-1051

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Analytical and numerical solutions of the inhomogeneous wave equation2004

    • Author(s)
      T.Matsuura
    • Journal Title

      The Australian Journal of Mathematical Analysis and Applications 1・1・7

      Pages: 1-18

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A method by transforms of variables for the first order nonlinear ordinary differential equations2004

    • Author(s)
      T.Tada
    • Journal Title

      Far East J.Math.Sci. 14・3

      Pages: 393-403

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Numerical real inversion formulas of the Laplace transform by using a Fredholm integral equation of the second kind

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

      Journal of Analysis and applications (In press)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Numerical real inversion formulas of the Laplace transform by using a Fredholm integral equation of the second kind

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

      Journal of Analysis and applications (In press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley-Wiener spaces

    • Author(s)
      T.Matsuura
    • Journal Title

      Applicable Analysis (掲載決定)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Analytical and numerical solutions of the inhomogeneous heat equation

    • Author(s)
      T.Matsuura
    • Journal Title

      Journal of Concrete and Applicable Mathematics(JCAAM) (掲載決定)

    • Related Report
      2005 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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