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Foundation of high accuracy computational methods on the multiple-precision computer environment and its applications to analysi of inverse problems

Research Project

Project/Area Number 19340022
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

ISO Yuusuke  Kyoto University, 情報学研究科, 教授 (70203065)

Co-Investigator(Kenkyū-buntansha) NISHIMURA Naoshi  京都大学, 情報学研究科, 教授 (90127118)
YAMAMOTO Yutaka  京都大学, 情報学研究科, 教授 (70115963)
SUGIMOTO Naozou  京都大学, 医学研究科, 教授 (20196752)
FUJIWARA Hiroshi  京都大学, 情報学研究科, 助教 (00362583)
HIGASHIMORI Nobuyuki  京都大学, 情報学研究科, 研究員 (10397573)
IMAI Hitoshi  徳島大学, ソシオテクノサイエンス研究部, 教授 (80203298)
NISHIDA Takaaki  早稲田大学, 理工学術院, 教授 (70026110)
OONISHI Kazuei  茨城大学, 理学部, 教授 (20078554)
YAMAMOTO Masahiro  東京大学, 数理科学研究所, 教授 (50182647)
NISHIDA Kotoba  鹿児島大学, 理学部, 助教 (10274838)
Research Collaborator MATSUDA Tetsuya  京都大学, 情報学研究科, 教授 (00209561)
OKAMOTO Hisashi  京都大学, 数理解析研究所, 教授 (40143359)
SAKAJYO Takashi  北海道大学, 理学研究院, 教授 (10303603)
NAKAMURA Gen  北海道大学, 理学研究院, 教授 (50118535)
TANUMA Kazumi  群馬大学, 工学研究科, 准教授 (60217156)
SHIROTA Kenji  愛知県立大学, 情報科学部, 准教授 (90302322)
NAKAO Mitsuhiro  九州大学, 数理学研究院, 教授 (10136418)
TOMOEDA Kenji  大阪工業大学, 工学部, 教授 (60033916)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥18,070,000 (Direct Cost: ¥13,900,000、Indirect Cost: ¥4,170,000)
Fiscal Year 2009: ¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2008: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2007: ¥6,500,000 (Direct Cost: ¥5,000,000、Indirect Cost: ¥1,500,000)
Keywords応用数学 / 数値解析 / 多倍長数値計算 / 応用解析学 / 逆問題解析 / 非適切問題解析 / 高精度シミュレーション / 逆Laplace変換 / 数値計算
Research Abstract

The multiple-precision computer environment has been considered as a new research tool which can bear progress of sciences and technologies in top. In this project, we have been succeeded in not only development of multiple-precision arithmetic but its applications to hard problems in inverse and ill-posed analysis. We have established so excellent results that we lead research trends in computational mechanics.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (17 results)

All 2010 2009 2008 2007

All Journal Article (17 results) (of which Peer Reviewed: 16 results)

  • [Journal Article] Recovering a Lame kernel in a viscoelastic equation by a single boundary measurement.2010

    • Author(s)
      Romanov, V.G.; Yamamoto, M.
    • Journal Title

      Appl.Anal. 89 no.3

      Pages: 377-390

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical real inversion of the Laplace transform by using a high-accuracy numerical method2009

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

      FURTHER PROGRESS IN ANALYSIS-Proceedings of the 6th International ISAAC Congress

      Pages: 574-583

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] An FMM for orthotropic periodic boundary value problems for Maxwell's equations2009

    • Author(s)
      Y.Otani, N.Nishimura
    • Journal Title

      Waves in Random and Complex Media vol.19

      Pages: 80-104

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-B{\' e}nard problems2009

    • Author(s)
      M.Kim, M.T.Nakao, Y.Watanabe, T.Nishida
    • Journal Title

      Numerische Mathematik Vol.111

      Pages: 389-406

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Inverse heat source problem from time distributing overdetermination.2009

    • Author(s)
      Sakamoto, Kenichi ; Yamamoto, Masahiro
    • Journal Title

      Appl. Anal. 88 no.5

      Pages: 735-748

    • Related Report
      2009 Final Research Report
    • 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

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Finite Difference Approximation of III-Posed Cauchy Problems2009

    • Author(s)
      Kotoba NISHIDA, Hiroshi FUJIWARA, Yuusuke ISO
    • Journal Title

      Theoretical and Applied Mechanics Japan 57

      Pages: 405-410

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical real inversion of the Laplace transform by using a high-accuracy numerical method2009

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

      Proceedings of the 6th International ISAAC Congress

      Pages: 574-583

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Real inversion formulas of the Laplace transform on weighted function spaces2008

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

      Complex Anal.Oper.Theory Vol.2(3)

      Pages: 511-521

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [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

      J.Anal. Appl. Vol.6(1)

      Pages: 55-68

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical solution to the Cauchy problem of the Laplace equation with noisy data.2008

    • Author(s)
      K.Onishi K.Shirota, T.Shigeta
    • Journal Title

      Theoretical and Applied Mechanics Japan Vol.57

      Pages: 481-486

    • NAID

      130004463713

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Finite Difference Approximations to the Poisson Equation in a Class of Analytic Functions2008

    • Author(s)
      Kotoba NIDHIDA
    • Journal Title

      Journal of Hyperbolic Differential Equations Vol.5, No.1

      Pages: 85-98

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Finite Difference Approximation of Tll-Posed Cauchy Problems2008

    • Author(s)
      Kotoba NISHIDA, Hiroshi FUJIWARA, Yuusuke ISO
    • Journal Title

      Theoretical and Applied Mechanics Japan Vol.57

      Pages: 405-410

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Real inversion formulas of the Laplace transform on weighted function spaces2008

    • Author(s)
      Fujiwara H., 他2名
    • Journal Title

      Complex Anal. Op. Th. Vol. 2, No. 3

      Pages: 511-521

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical treatment of analytic continuation on multiple-precision arithmetic2007

    • Author(s)
      H.Fujiwara, H.Imai, T.Takeuchi, Y.Iso
    • Journal Title

      Hokkaido Math.J. Vol.36(4)

      Pages: 837-847

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Application of multiple-precision arithmetic to direct numerical computation of inverse acoustic scattering2007

    • Author(s)
      H.Fujiwara, Y.Iso
    • Journal Title

      J.Physics Conference Series Vol.73 Article No.012007

    • Related Report
      2009 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)
      Fujiwara H, 他3名-
    • Journal Title

      J. Anal. Appl. Vol.5,No.2

      Pages: 123-136

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed

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

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