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A DEVELOPMENT OF THE CRITERION METHOD FOR GENERALIZED DIAGONALLY DOMINANT MATRICES AND A STUDY OF THE ITERATIVE METHOD FOR PARALLEL PROCESSING

Research Project

Project/Area Number 11640144
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

USUI Masataka  OKAYAMA UNIVERSITY OF SCIENCE, FACULTY OF INFORMATICS, ASSIST.PRO, 総合情報学部, 助教授 (40068888)

Co-Investigator(Kenkyū-buntansha) HIRANO Hiroyuki  OKAYAMA UNIVERSITY OF SCIENCE, FACULTY OF ENGINEERING, LECTURER, 工学部, 講師 (60264115)
OKAMOTO Naotaka  OKAYAMA UNIVERSITY OF SCIENCE, FACULTY OF ENGINEERING, PROFESSOR, 工学部, 教授 (00068909)
NIKI Hiroshi  OKAYAMA UNIVERSITY OF SCIENCE, FACULTY OF INFORMATICS, PROFESSOR, 総合情報学部, 教授 (30068879)
KOHNO Toshiyuki  OKAYAMA UNIVERSITY OF SCIENCE, FACULTY OF INFORMATICS, ASSISTANT, 総合情報学部, 助手 (90309534)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 1999: ¥1,400,000 (Direct Cost: ¥1,400,000)
KeywordsITERATIVE CRITERION / ITERATIVE METHOD / H-MATRIX / GENERALIZED DIAGONALLY DOMINANT MATRIX (GDDM) / GAUSS-SEIDEL TYPE / DIRECT TYPE / 反復法 / 並列処理
Research Abstract

The numerical computation is carried out to solve the linear systems Ax=b by using the iterative method. In this project we presented new criterion and showed that our criterion is simpler than other's with some numerical experiments. Further we tested the effectivity of the proposed method, and we obtained that our method is effective in solving the linear systems. Thus, we developed a simple method for judging II-matrix.
In 1999th, we improved the iteration type as the criterion of the Generalized Diagonally Dominant Mtrix (G.D.D.M.). Then, We are adapted this method to some examples, and obtained better results.
In 2000th, we are adapted this criterion to some practical examples , and furthermore we confirmed the availability of this method. So we became a ware of an own peculiarity of G.D.D.M.Therefore we test to develop the direct criterion for some II-matrices and succeeded in developping the method less than Yiming Gao, s.
Coming our subject is testing some numerical experiment for much more H-matrices and to prove the mathematical validity.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (21 results)

All Other

All Publications (21 results)

  • [Publications] L.Lei: "A Nonparameter Criterion for Generalized Diagonally Dominant Matrices"International Journal of Comput.Math.. 71. 267-275 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Hirano: "Application of the Preconditioning Iterative Method of Computational Fluid Dynamics."Proceedings of RIKEN symposium Linear Algebra and its Applications. 27-34 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Kohno: "An iterative test for H-matrix"Journal of Computational and Applied Mathematics. 115. 349-355 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Niki: "The Preconditioned Gauss-Seidel Method"Proceedings of the 16th IMACS World Congress 2000 on Scientific Computation, Applied Mathematics and Simulation. (CD-ROM). 1-6 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Hirano: "Numerical Computation of Natural Convection with The Preconditioning Iterative Method"Proceedings of the 4th JSME-KSME Thermal Engineering Conference. 112. 233-238 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Hirano: "Comparison Theorems for The Preconditioning Gauss-Seidei Method.(Invited Paper)"Proceedings of the First International Conference on Informantion.. 25-31 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Ojiro: ""A new direct test for H-matrix""Information. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] L.Lei: "A Nonparameter Criterion for Generalized Diagonally Dominant Matrices"International Journal of Comput.Math.. 71. 267-275 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Hirano: "Application of the Preconditioning Iterative Method of Computational Fluid Dynamics"Proceedings of RIKEN symposium Linear Algebra and its Applications. 27-34 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Kohno: "An iterative test for II-matrix"Journal of Computational and Applied Mathematics. 115. 349-355 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Niki: "The Preconditioned Gauss-Seidel Method"Proceedings of the 16th IMACS World Congress 2000 on Scientific Computation, Applied Mathematics and Simulation. (CD-ROM). 1-6 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Hirano: "Numerical Computation of Natural Convection with the Preconditioning Iterative Method"Proceedigs of the 4th JSMEKSME Thermal Engineering Conference. Vol.2. 233-238 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] H.Hirano: ""Comparison Theorems for the Preconditioning Gauss-Seidel Method", (Invited Paper)"Proceedings of the First International Conference on Information. 25-31 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Ojiro: "A new direct test for H-matrix"Information. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] L.Lei: ""A Nonparameter Criterion for Generalized Diagonally Dominant Matrices""International Journal of Comput.Math.. 71. 267-275 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Hirano: ""Application of the Preconditioning Iterative Method of Computational Fluid Dynamics","Proceedings of RIKEN symposium Linear Algebra and its Applications. 27-34 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Kohno: ""An iterative test for H-matrix""Journal of Computational and Applied Mathematics. 115. 349-355 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Niki: ""The Preconditioned Gauss-Seidel Method""Proceedings of the 16th IMACS World Congress 2000 on Scientific Computation, Applied Mathematics and Simulation (CD-ROM). 1-6 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Hirano.: ""Numerical Computation of Natural Convection with The Preconditioning Iterative Method""Proceedings of the 4th JSME-KSME Thermal Engineering Conference. 112. 233-238 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Hirano: ""Comparison Theorems for The Preconditioning Gauss-Seidel Method", (Invited Paper)"Proceedings of the First International Conference on Information.. 25-31 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Ojiro: ""A new direct test for H-matrix""Information. (to appear).

    • Related Report
      2000 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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