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1993 Fiscal Year Final Research Report Summary

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
KeywordsLarge sparse matrix / Preconditioned CG method / Parallel algorithm / Matrix eigenvalue problem / Lanczos algorithm / III - posed problem / Free boundary problem / Natural convection
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.

  • Research Products

    (14 results)

All Other

All Publications (14 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 1995-03-27  

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