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Algorithms for Large Scale Linear Systems in the Numerical Simulation

Research Project

Project/Area Number 04640209
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionUniversity of Tsukuba

Principal Investigator

NATORI Makoto  Inst.Info.Sci., Univ.of Tsukuba, Professor, 電子・情報工学系, 教授 (70013745)

Co-Investigator(Kenkyū-buntansha) IMAI Hitoshi  Fac.Eng., Univ.of Tokushima, Assoc.Prof., 工学部, 助教授 (80203298)
SAKURAI Tetsuya  Inst.Info.Sci., Univ.of Tsukuba, Assis.Prof., 電子・情報工学系, 講師 (60187086)
KITAGAWA Takashi  Inst.Info.Sci., Univ.of Tsukuba, Assoc.Prof., 電子・情報工学系, 助教授 (60153095)
INAGAKI Toshiyuki  Inst.Info.Sci., Univ.of Tsukuba, Assoc.Prof., 電子・情報工学系, 助教授 (60134219)
IKEBE Yasuhiko  Inst.Info.Sci., Univ.of Tsukuba, Professor, 電子・情報工学系, 教授 (10114034)
Project Period (FY) 1992 – 1993
Project Status Completed (Fiscal Year 1993)
Budget Amount *help
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1993: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1992: ¥700,000 (Direct Cost: ¥700,000)
KeywordsLarge sparse matrix / Preconditioned CG method / Parallel algorithm / Matrix eigenvalue problem / Lanczos algorithm / III - posed problem / Free boundary problem / Natural convection / 大規模連立一次方程式 / 正則化法 / ブロックランチョス法
Research Abstract

In this research, algorithms to solve large scale linear systems appeared in the numerical simulation were investigated.
(1)We investigated preconditioned conjugate gradient methods to solve large scale linear systems of equations. Especially, We considered BiCGSTAB method which is known to be stable for asymmetric matrics. We developed a new preconditioner which enables parallel processing.
(2)We investigated Lanczos algorithm to compute eigenvalus of large sparse matrices. Especially, we concidered the block Lanczos algorithm for matrices which have degenerate eigenvalues. We developed a new reorthoganalization mehod for the block Lanczos algorithm.
(3)We investigated regularization methods for ill - posed problems. We developed new algorithms to estimate the value of the optimal regularization parameters.
(4)We carryed out the numerical simulations of solidification problems with change of valume and natural convection problems with a free surface.

Report

(3 results)
  • 1993 Annual Research Report   Final Research Report Summary
  • 1992 Annual Research Report
  • Research Products

    (28 results)

All Other

All Publications (28 results)

  • [Publications] H.Iguchi: "Reorthogonalization in the block Lanczos algorithm" Bulletin of the Greek Mathematical Society. 33. 25-39 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Kitagawa: "New approaches to the optimal regularization" Inverse Problems in Engineering Mechanics. 21-26 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] H.Imai: "An application of the fuzzy theory for a ill-posed problem" Inverse Problems in Engineering Mechanics. 31-38 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 細田陽介: "不適切問題に対するMAICE-DP法による最適正則化法" 日本応用数理学会論文誌. 3. 47-58 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Hanada: "Numerical Computations for Solidification Problem with Moving Surface" Nonlinear Mathematical Problems in Industry. 1. 17-38 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Zhou Weidong: "Numerical Study of Natural Convection with a Free Surface by a Spectral Method" Nonlinear Mathematical Problems in Industry. 1. 49-60 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 名取亮: "線形計算" 朝倉書店, 141 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] 池辺八洲彦・稲垣敏之: "数値解析入門" 昭晃堂, 188 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] H.Iguchi: "Reorthogonalization in the block Lanczos algorithm" Bulletin of the Greek Mathematical Society. Vol.33. 25-39 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Kitagawa: "New approaches to the optimal regularization" Inverse Problems in Engineering Mechanics. 21-26 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] H.Imai: "An application of the fuzzy theory for a III-posed problem" Inverse Problems in Engineering Mechanics. 31-38 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Y.Hosoda: "Optimal Regularization Method MAICEDP for III-posed Problems" Transactions of the Japan Society for Industrial and Applied Mathematics. Vol.3. 47-58 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Hanada: "Numerical Computations for Solidification Problem with Moving Surface" Nonlinear Mathematical Problems in Industry. Vol.1. 17-38 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Zhou Weidong: "Numerical Study of Natural Convection with a Free Surface by a Spectral Method" Nonlinear Mathematical Problems in Industry. Vol.1. 49-60 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] T.Kitagawa: "New approaches to the optimal regularization" Inverse Problems in Engineering Mechanics. 21-26 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] H.Imai: "An application of the fazzy theory for a ill-posed problem" Inverse Problems in Engineering Mechanics. 31-38 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 細田陽介: "不適切問題に対するMAICE-DP法による最適正則化法" 日本応用数理学会論文誌. 3. 47-58 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] T.Hanada: "Numerical Computations for Solidification Problem with Moving Surface" Nonlinear Mathematical Problems in Industry. 1. 17-38 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] H.Imai: "Numerical Computations of Free Boundary Problem using the Spectral Method" Nonlinear Mathematical Problems in Industry. 1. 39-47 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Zhou Weidong: "Numerical Study of Natural Convection with a Free Surface by a Spectral Method" Nonlinear Mathematical Problems in Industry. 1. 49-60 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 名取 亮: "線形計算" 朝倉書店, 141 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 池辺八洲彦,稲垣敏之: "数値解析入門" 昭晃堂, 188 (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] 細田 陽介: "Lカーブによる不適切問題の最適正則化について" 日本応用数理学会論文読. 2. 55-67 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Kitagawa: "New approaches to the optimal regularization" Proc.IUTAM Symp.Inv.Prob.Eng.Mech.(1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Hanada: "Numerical Computations for Solidification Problem with Moving Surfaces" Proc.Int.Symp.Nonlin.Math.Prob.Industry. (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] Zhou Weidong: "A Spectral Method to Calculate Natural Couvection with a Free Surface" Proc.Int.Symp.Nonlin.Math.Prob.Industry. (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] H.Imai: "Numerical Computation of Free Boundary Problem using the Spectral Method" Proc.Int.Symp.Nonlin.Math.Prob.Industry. (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] T.Kitagawa: "A Comparison Between the two classes of methods for the optimal regularization" Proc.Int.Conf.Comp.Eng.Science. (1992)

    • Related Report
      1992 Annual Research Report

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Published: 1992-04-01   Modified: 2016-04-21  

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