Parallelization of Iterative Method

迭代法的并行化

• 批准号: 09640305
• 负责人: NIKI Hiroshi
• 金额: $ 1.73万
• 依托单位: OKAYAMA UNIVERSITY OF SCIENCE
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640305/
• 关键词: NUMERICAL COMPUTATION; ITERATIVE METHOD; PRECONDITIONING; 数値解法; 移流拡散問題; 数値解析; 誤差解析

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.

进行数值计算以使用迭代方法来解决线性系统。在本项目中，我们介绍了新的预处理方法，并表明我们的方法在一些数值实验中比SOR方法更快。我们的方法是具有正参数的预处理矩阵的高斯 - 西德尔方法。我们还得出了我们提出的方法的收敛定理。此外，我们获得了预处理矩阵的最佳参数的估计公式。此外，我们测试了所提出的方法和对流扩散问题的效果，我们获得了我们的方法有效解决这样的实际问题。众所周知，如果系数矩阵A具有H-矩阵，那么迭代方法就可以使用解决线性系统。因此，我们开发了一种简单的先验方法来判断h-matrix。它已指出，我们的预处理方法有效地提高了在科学和工程领域的线性系统解决线性系统的性能。

项目成果

Toshiyuki Kohno: "Improving the modified Gauss-Seidel Method for H-matrices"Linear Algebra and its Applicatopns. 83. 113-123 (1997)

Toshiyuki Kohno：“改进 H 矩阵的修正高斯-赛德尔方法”线性代数及其应用。

Hisashi Kotakemori: "A generalization of the Adaptive Gauss-Seidel method for Z-matrices"Intern. J. Computer Math.. 64. 317-326 (1997)

Hisashi Kotakemori：“Z 矩阵的自适应高斯-赛德尔方法的推广”实习生。

S.Kanno: "Adaptive acceleration of the Durand-Kerner method" IEICE Trans.on Fund.of Elect.,C.and C.Science. (印刷中). (1999)

S.Kanno：“Durand-Kerner 方法的自适应加速”IEICE Trans.on Fund.of Elect.、C.and C.Science（出版中）。

Y.Iwasaki: "Algebraic and Geometrical Aspects on the Chinese Remainder Theorem" Information. 1[2]. 33-45 (1998)

Y.Iwasaki：“中国剩余定理的代数和几何方面”信息。

Emiko Ishiwata: "New Criteria for Generalized Diagonally Dominant Matrices"Intern. J. Computer Math. 69. 391-396 (1998)

Emiko Ishiwata：“广义对角占优矩阵的新标准”实习生。