1999 Fiscal Year Final Research Report Summary
Parallelization of Iterative Method
| Project/Area Number |
09640305
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | OKAYAMA UNIVERSITY OF SCIENCE |
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Principal Investigator |
NIKI Hiroshi OKAYAMA UNIV. OF SCIENCE, FACULTY OF INFORMATICS, PROFESSOR, 総合情報学部, 教授 (30068879)
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| Co-Investigator(Kenkyū-buntansha) |
IWASAKI Yoshimitsu OKAYAMA UNIV. OF SCIENCE, FACULTY OF INFORMATICS, PROFESSOR, 総合情報学部, 教授 (70278901)
SAWAMI Hideo OKAYAMA UNIV. OF SCIENCE, FACULTY OF INFORMATICS, PROFESSOR, 総合情報学部, 教授 (70098581)
OKAMOTO Naotaka OKAYAMA UNIV. OF SCIENCE, FACULTY OF INFORMATICS, PROFESSOR, 工学部, 教授 (00068909)
菅野 幸夫 岡山理科大学, 総合情報学部, 講師 (10289134)
HIRANO Hiroyuki OKAYAMA UNIV. OF SCIENCE, FACULTY OF INFORMATICS, LECTURER, 工学部, 講師 (60264115)
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| Project Period (FY) |
1997 – 1999
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| Keywords | NUMERICAL COMPUTATION / ITERATIVE METHOD / PRECONDITIONING / 数値解法 / 移流拡散問題 |
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| Research Abstract |
The numerical computation was carried out to solve the linear system by using the iterative method.
In this project we presented the new preconditioning iterative method and showed that our method is faster than SOR method with some numerical experiments. Our method is the Gauss-Seidel Method for the preconditioning matrix with a positive parameter. We also derived convergence theorem of our proposed method. Moreover, we obtained the estimation formula of optimum parameter for the preconditioned matrix. Further we tested the effectivity of the proposed method and convective diffusion problem, and we obtained that our method is effective in solving such a practical problem.
It is well known that if coefficient matrix A has H-matrix, then the iterative method is able to use solving the linear systems. Thus, we developed simple a priori method for judging H-matrix.
It has been pointed out that our preconditioning iterative method is effective to improve the performance to solve the linear system in various fields of science and engineering.
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