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Development of Algorithm for Eigenvalue Analysis of Very Large Matrices

Research Project

Project/Area Number 05555026
Research Category

Grant-in-Aid for Developmental Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field Engineering fundamentals
Research InstitutionHOKKAIDO UNIVERSITY

Principal Investigator

NAKAYAMA Tsuneyoshi (1994-1995)  Hokkaido Univ., Fac. of Eng., Pro., 工学部, 教授 (80002236)

矢久保 考介 (1993)  北海道大学, 工学部, 助教授 (40200480)

Co-Investigator(Kenkyū-buntansha) KAKUMA Seiichi  Hokkaido Univ., Fac. of Eng., Instructor, 工学部, 助手 (90204338)
MIZUNO Seiji  Hokkaido Univ., Fac. of Eng., Lecturer, 工学部, 講師 (90222322)
TAKANO Motohiro  CSK Limited, AI UNIX Laboratory, Researcher, 研究員
YAKUBO Kousuke  Hokkaido Univ., Fac. of Eng., Asso. Pro., 工学部, 助教授 (40200480)
Project Period (FY) 1993 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥5,000,000 (Direct Cost: ¥5,000,000)
Fiscal Year 1995: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1994: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1993: ¥3,200,000 (Direct Cost: ¥3,200,000)
KeywordsEigenvalue / Large Matrix / Algorithm / 並列処理 / 高速アルゴリズム / スーパー・コンピュータ
Research Abstract

This research project aims to develope the powerful algorithm suitable for very large matrices of the order of 10^7. The method is based on the mapping of the eigenvalue problem to lattice dynamics. The method is unique, compared with the other well known methods like the Lanezos method. Namely, the time-consuming part is mainly used for solving the time-development equation of motion. The efficiency was demonstrated by applying fractal systems and the mode analysis of sophistcated waveguides.

Report

(4 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • 1993 Annual Research Report
  • Research Products

    (35 results)

All Other

All Publications (35 results)

  • [Publications] T. Terao: "Double-peak Strucutre of the Dynamical Structure Factor in Diluted Hesenberg Antiferromagnets" Phys. Rev. B. 51. 11479-11483 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T. Nakayama: "Elastic Vibrations of Fractal Networks" Jpn. J. Appl. Phys.34. 2519-2524 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Y. Hobiki: "Spectral Distribution of Drums with Fractal Perimeters: The Weyl-Berry-Lapidus Conjecture" Phys. Rev. B. 52. R1310-R1312 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H. Noro: "Mode Analysis of Optical Waveguides: A New Approach" Optics Letters. 20. 1227-1229 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T. Nakayama: "Computing Very Large Matrices: The Forced Oscillator Method" Computational Physics as a New Frontier in Condensed Matter Research. 21-33 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T. Terao: "Power-law Dependence on Frequency of the Raman-scattering Intensity of Percolating Networks" Phys. Rev. B. 53,((in press). (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K. Takubo: "Fracton Decay in Nonlinear Fractal Systems" Physica B. (in press). (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T. Terao: "An Efficient Method For Computing Dynamic Response Functions for Large-scale Vibrational Systems" Physica B. (in press). (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Y. Hobiki: "Fractal Drums and the Weyl-Berry-Lapidus Conjecture" Physica B. (in press). (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Terao: "Double-peak Structure of the Dynamical Structure Factor in Diluted Heisenberg Antiferromagnets" Phys. Rev. B. 51-17. 11479-11483 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Nakayama: "Elastic Vibrations of Fractal etworks" Jpn. J.Appl. Phys.34-50. 2519-2524 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Y.Hobiki: "Spectral Distribution of Drums with Fractal Perimeters : The Weyl-Berry-Lapidus Conjecture" Phys. Rev. B. 52-2. R1310-R1312 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Noro: "Mode Analysis of Optical Waveguides : a New Approach" Optics Letters. 20-11. 1227-1229 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Nakayama: "Computing Very Large Matrices : The Forced Oscillator Method" Computational Physics as a New Frontier in Condensed Matter Research. 21-33 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Terao: "Power-law Dependence on Frequency of the Raman-scattering Intensity of Percolating Networks" Phys. Rev. B. 53-6 (in press). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Yakubo: "Fracton Decay in Nonlinear Fractal Systems" Physica B. (in press). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Terao: "An Efficient Method for Computing Dynamic Response Functions for Large-scale Vibrational Systems" Physica B. (in press). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Y.Hobiki: "Fractal Drums and the Weyl-Berry-Lapidus Conjecture" Physica B. (in press). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] T.Terao: "Double-peak Strucutre of the Dynamical Structure Factor in Diluted Heisenberg Antiferromagnets" Phys.Rev.B. 51. 11479-11483 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T.Nakayama: "Elastic Vibrations of Fractal Networks" Jpn.J.Appl.Phys.34. 2519-2524 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Y.Hobiki: "Spectral Distribution of Drums with Fractal Perimeters: The Weyl-Berry-Lapidus Conjecture" Phys.Rev.B. 52. R1310-R1312 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] H.Noro: "Mode Analysis of Optical Waveguides: a New Approach" Optics Letters. 20. 1227-1229 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T.Nakayama: "Computing Very Large Matrices: The Forced Oscillator Method" Computational Physics as a New Frontier in Condensed Matter Research. 21-33 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] T.Terao: "Power-law Dependence on Frequency of the Raman-scattering Intensity of Percolating Networks" Phys.Rev.B. 53(in press). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] Nakayama: "Dynamical Properties of Feactal Networks:Scaling,Numerical Simulations,and Physical Realizations" Rev.Mod.Phys,. 66. 381-443 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Yakubo: "Spin Wave Dynamics of Percolating Heisenberg Antiferromagnets" J.Phys.Soc.Jpn.63. 3431-3441 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] T.Terao: "Numerical Method for Large-Scale Non-Hermitian Matrices and Its Application to Percolating Heisenberg Antiferromagners" Phys.Rev.E. 50. 566-576 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] T.Terao: "Scaling Properties of the Dynamical Structure Factor of Percolating Heisenberg Antiferromagnets" Phys.Rev.B. 49. 12281-12284 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] T.Nakayama: "Fracton Dimensions for Elastic and Antiferromagnetic Percolating Networks,Soft Order in Physical Systems" NATOASI Series,Plenum Press,New York. 181-184 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] K. Yakubo, T. Terao, T. Nakayama: "Antiferromagnetic fractons and its spectral dimension" Fractals. 1. 881-885 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] K. Yakubo, T. Terao, T. Nakayama: "Spectral dimension of percolating Heisenberg antiferromagnets" J. Phys. Soc. Jpn.62. 2196-2199 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] T. Nakayama, K. Yakubo, M. Takano: "Strong localization of photons in aperiodic optical waveguides:A Numerical realization" Phys. Rev. B. 47. 9249-9253 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] T. Terao, K. Yakubo, T. Nakayama: "Dynamical structure factor and its scaling property of percolating Heisenberg antiferromagnets" Phys. Rev. B. 49(in press). (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] T. Nakayama: "Fracton dimensions for elastic and antiferromagnetic percolating networks" NATO Adyanced Institute Series, Soft order in physical systems, ed. R. Bruinsma & Y. Rabin(Plenum Press)(in press). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] T. Nakayama, K. Yakubo, R. Orbach: "Dynamical properties of fractal networks: scaling, numerical simulations, and physical realizations" Rev. Mod. Phys.66(in press). (1994)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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