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Research on the double exponential transformation subroutine package

Research Project

Project/Area Number 12640119
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 InstitutionTokyo Denki University (2001-2002)
Kyoto University (2000)

Principal Investigator

MORI Masatake  Tokyo Denki University, Department of Mathematical Sciences, Professor, 理工学部, 教授 (20010936)

Co-Investigator(Kenkyū-buntansha) OOURA Takuya  Kyoto University, Research Institute for Mathematical Sciences, Research Associate, 数理解析研究所, 助手 (50324710)
降旗 大介  京都大学, 数理解析研究所, 助手 (80242014)
Project Period (FY) 2000 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2000: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsdouble exponential transformation / numerical integration / variable transformation / subroutine package / 二重指数関数型公式 / DE変換 / 数値解析 / 最適公式
Research Abstract

Suppose that an integral over (a, b) is given. Then it is known that, if you transform the integral using a function which maps (a, b) onto (-∽, ∽) and apply the trapezoidal rule with an mesh size to the integral after the transformation you will get a result with high precision. In 1974 H. Takahashi and M. Mori, the head investigator, found that if you choose a transformation by which the function after the transformation decays double exponentially the result will be the best, and they proposed several specific transformations useful for numerical evaluation of various kind of integrals. A formula obtained in this way is called the double exponential formula.
The purpose of the present research project is to provide users with a subroutine package of the double exponential formulas. The package we developed includes subroutines for integrals over a finite interval, integrals with end point singularity, integrals of a slowly decaying function over (0, ∽), Fourier type integrals of a slowly decaying function, and it also includes automatic integrators. An automatic integrator is a subroutine that, when the user gives a function subprogram defining the integrand and an error tolerance, returns a result whose error is expected to lie in the tolerance. We prepared a manual which shows how to use the package and printed it in the report of the present research together with the entire source code written in FORTRAN.

Report

(4 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • Research Products

    (25 results)

All Other

All Publications (25 results)

  • [Publications] Takuya Ooura: Journal of Computational and Applied Mathematics. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Masatake Mori: "Optimality of the double exponential transformation in numerical analysis"Sugaku Expositions. 14. 103-123 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Saburou Saitoh: Complex Variables. 45. 387-393 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Masatake Mori: "The double exponential transformation in numerical analysis"Journal of Computational and Applied Mathematics. 127. 287-296 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takuya Ooura: Journal of Computational and Applied Mathematics. 130. 259-270 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Kaname Amano: Contributions in Analytic Extension Formulas and their Applications. 15-25 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Ooura, Takuya: "A generalization of the continuous Euler transformation and its application to numerical quadrature"J. Comput. Appl. Math. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Mori, Masatake: "Optimality of the double exponential transformation in numerical analysis"Sugaku Expositions. 14. 103-123 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Saitoh, Saburou and Mori, Masatake: "Representations of analytic functions in terms of local values by means of the Riemann mapping function"Complex Variables. 45. 387-393 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Mori, Masatake and Sugihara Masaaki: "The double exponential transformation in numerical analysis"J. Comput. Appl. Math.. 127. 287-296 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Ooura, Takuya: "A Continuous Euler transformation and its application to the Fourier transform of a slowly decaying function"J. Comput. Appl. Math.. 130. 259-270 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Amano, Kaname, Asaduzzaman, M., Ooura, Takuya and Saitoh, Saburou: "Representation of Analytic Functions on Typical Domains in Terms of Local Values and Truncation Error Estimates, Contributions in Analytic Extension Formulas and their Applications"Kluwer Academic Publisher. 15-25 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Takuya Ooura: "A generalization of the continuous Euler transformation and its application to numerical quadrature"Journal of Computational and Applied Mathematics. (印刷中).

    • Related Report
      2002 Annual Research Report
  • [Publications] Masatake Mori: "Optimality of the double exponential transformation in numerical analysis"Sugaku Expositions. 14. 103-123 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Saburou Saitoh: "Representations of analytic functions in terms of local values by means of the Riemann mapping function"Complex Variables. 45. 387-393 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Masatake Mori: "The double exponential transformation in numerical analysis"Journal of Computational and Applied Mathematics. 127. 287-296 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Takuya Ooura: "A continuous Euler transformation and its application to the Fourier transform of a slowly decaying function"Journal of Computational and Applied Mathematics. 130. 259-270 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Kaname Amano: "Representation of analytic functions on typical domains in terms of local values and truncation error estimates"Contributions in Analytic Extension Formulas and their Applications. 15-25 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] 森 正武: "The double expenential transformation in nunerical analysis"Journal of Computational and Applied Mathematics. 127. 287-296 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 大浦拓哉: "A continuous Euler transformation and its application to the Fourier transform of a slowly decaying function"Journal of Computational and Applied Mathematics. 130. 259-270 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 斎藤三郎: "Representations of analytic functions in terms of local values by means of the Riemann mapping function"Complex Variables. 45. 387-393 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 森 正武: "Optimality of the double exponential transformation in numerical analysis"Sugaku Expositions. 14. 103-123 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 森正武: "The double exponential transformation in numerical analysis"J.Comput.Appl.Math.. 127. 287-296 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] 斎藤三郎: "Representations of analytic functions in terms of local values by means of the Riemann mapping function"Complex Variables. (印刷中).

    • Related Report
      2000 Annual Research Report
  • [Publications] 森正武: "Optimality of the double exponential transformation in numerical analysis"Sugaku Expositions. (印刷中).

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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