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2005 Fiscal Year Final Research Report Summary

The synthetic research for the basic iterative method for the non-diagonal dominant matrix.

Research Project

Project/Area Number 15540144
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 InstitutionOkayama University of Science

Principal Investigator

NIKI Hiroshi  Okayama University of Science, Professor, 客員教授(常勤) (30068879)

Co-Investigator(Kenkyū-buntansha) AWAMI Hideon  Okayama University of Science, Informatics, Professor, 総合情報学部, 教授 (70098581)
HAMAYA Yoshihiro  Okayama University of Science, Informatics, Professor, 総合情報学部, 教授 (40228549)
CHEN Xiaojun  Hirosaki University, Science and Technology, Professor, 理工学部, 教授 (70304251)
ABE Kuniyoshi  Gifu Shoutoku University, Economics and Information, Assistant professor, 経済情報学部, 助教授 (10311086)
KOHNO Toshiyuki  Okayama University of Science, Infomatics, Assistant, 総合情報学部, 助手 (90309534)
Project Period (FY) 2003 – 2005
Keywordsaccuracy / H-matrix / preconditioning / the iterative method / finite difference / the CG method / Kryllov su space method / NCP function
Research Abstract

(1)Development of the new preconditioning matrix
We developed the new preconditioning matrix. Using the new preconditioning matrix can be accelerate of convergence of the classical Gauss-Seidel method. Moreover, it is possible to solve a non-diagonal dominant matrix which is impossible to apply the iterative method. On the other hand, Kohno developed other type's preconditioning matrix and obtained many effective results. The proposed method is excellent in iterative numbers and CPU time as compared with the ICCG method.
(2)Development of criterion of the H-matrix.
The H-matrix is very important for the solution of linear systems of algebraic equations by the iterative methods. But there is not criterion for the H-matrix. We developed the iterative criterion as new criterion. This method is our completely original. However, many iteration numbers are needed in judge to all H-matrix. In order to conquer this fault, we discovered new iterative criterion
(3)We give new error bounds for the linear complementarity problem where the involved matrix is a P-matrix. Computation of rigorous error bounds can be turned into P-matrix linear interval system. Moreover, for the involved matrix being an H-matrix with positive diagonals, an error bound can be found by solving a linear system of equations which is sharper than the Mathias-Pang error bound.

  • Research Products

    (16 results)

All 2005 2004

All Journal Article (16 results)

  • [Journal Article] A Variable Preconditioning with the SOR Method for the GCR-like Methods2005

    • Author(s)
      K.Abe, S.Zhnag
    • Journal Title

      International J. of Numerical Analysis and Modeling 2

      Pages: 147-162

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Finite Difference Smoothing Solution of Nonsmooth Constrained Optimal Control Problems2005

    • Author(s)
      X.Chen
    • Journal Title

      Functional Analysis and Optimization 26

      Pages: 49-68

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A smoothing implicit programming approach for solving a class of stochastic generalized semi-infinite programming problems2005

    • Author(s)
      C.Ling, X.Chen, M.Fukushima, L.Qi
    • Journal Title

      Pacific Journal of Optimization 1

      Pages: 127-145

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The behavior of micro-scaled Brownian particles in a cylinder under natural- and magnetic-convection flow field of air2005

    • Author(s)
      X.Wang, T.Tagawa, H.Ozoe, H.Hrano, Q.Wang
    • Journal Title

      Numerical Heat Transfer 47

      Pages: 353-373

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A smoothing implicit programming approach for solving a class of stochastic generalized semi-infinite programming problems.2005

    • Author(s)
      C.Ling, X.Chen, M.Fukushima, L.Qi
    • Journal Title

      Pacific.Journal of Optimization vol.1

      Pages: 127-145

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The behavior of micro-scaled Brownian particle in a cylinder under natural-and magnetic-convection flow field of air.2005

    • Author(s)
      X.Wang, T.Tagawa, H.Ozoe, H.Hirano, Q.Wang
    • Journal Title

      Numerical Heat Transfer vol.47

      Pages: 353-373

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A direct criterion for H-matrix.2005

    • Author(s)
      H.Niki, K.Tomura, M.Usui, L.Li, M.Sugihara
    • Journal Title

      Transactions of the Japan Society for Industrial and Applied Mathematics(in Japanese) vol.15

      Pages: 45-58

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On the adaptive preconditioned iterative method.2005

    • Author(s)
      T.Kohno
    • Journal Title

      Transactions of the Japan Society for Industrial and Applied Mathematics(in Japanese) vol.15

      Pages: 45-58

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Finite Difference smoothing Solution of Non-smooth Constrained Optimal Control Problems.2005

    • Author(s)
      X.Chen
    • Journal Title

      Functional Analysis and Optimization vol.6

      Pages: 49-68

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A variable preconditioning using the SOR method for GCR-like methods.2005

    • Author(s)
      K.Abe, S.Zhan
    • Journal Title

      Int.J.of Numerical Analysis and Modeling vol.2

      Pages: 147-161

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A Two-step Preconditioning Method for Solving Dense Linear Systems2004

    • Author(s)
      H.Kotakemori, H.Niki, N.Okamoto
    • Journal Title

      Int. J. Computational Fluid Dynamics 18

      Pages: 93-99

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Bifurcation of almost periodic solutions in difference equations2004

    • Author(s)
      Y.Hamaya
    • Journal Title

      Journal of Difference Equations and Applications 10

      Pages: 257-297

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A two step Preconditioning Method for Solving Dense Linear Systems.2004

    • Author(s)
      H.Kotakemori, H.Niki, M.Okamoto
    • Journal Title

      International J.Fluid Dynamics vol.18

      Pages: 93-99

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Bifurcation of almost periodic solutions in difference equations.2004

    • Author(s)
      H.Hamaya
    • Journal Title

      J.of Difference Equations and Applications vol.10

      Pages: 257-297

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The survey of preconditioners used accelerating the rate of convergence in the Gauss-Seidel method.2004

    • Author(s)
      H.Niki, K.Harada, M.Morimoto, M.Sakakihara
    • Journal Title

      Journal of Computational and Applied Mathematics vol.164-165

      Pages: 587-600

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Preconditioned Iterative Methods for Linear Equations Arising from the Boundary Element Method.2004

    • Author(s)
      N.Sakakihara, M.Morimoto, H.Niki, M.Okamoto.
    • Journal Title

      Int.J.Computational Fluid Dynamics vol.18

      Pages: 625-630

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2007-12-13  

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