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

广义对角主矩阵判据方法的发展及并行处理迭代方法的研究

• 批准号: 11640144
• 负责人: USUI Masataka
• 金额: $ 1.79万
• 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: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640144/
• 关键词: ITERATIVE CRITERION; ITERATIVE METHOD; H-MATRIX; GENERALIZED DIAGONALLY DOMINANT MATRIX (GDDM); GAUSS-SEIDEL TYPE; DIRECT TYPE; 反復法; 並列処理

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.

用迭代法对线性方程组Ax=B进行了数值计算。在本项目中，我们提出了新的准则，并通过一些数值实验表明我们的准则比其他准则更简单。进一步对该方法的有效性进行了验证，结果表明该方法在求解线性方程组时是有效的。在1999年，我们改进了广义对角占优矩阵（G.D.D.M.）的迭代型判据。在2000年，我们将该准则应用于一些实际的算例，进一步证实了该方法的有效性。因此，我们尝试对一些II-矩阵建立了直接判别法，并成功地发展了比高一鸣等人的方法更少的方法。接下来我们的课题是对更多的H-矩阵进行数值实验，并证明其数学有效性。

项目成果

H.Hirano: ""Comparison Theorems for The Preconditioning Gauss-Seidel Method", (Invited Paper)"Proceedings of the First International Conference on Information.. 25-31 (2000)

H.Hirano：““预处理高斯-赛德尔方法的比较定理”，（特邀论文）”第一届国际信息会议论文集.. 25-31 (2000)

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

L.Lei：“广义对角占优矩阵的非参数准则”International Journal of Comput.Math.. 71. 267-275 (1999)

T.Kohno: "An iterative test for H-matrix"Journal of Computational and Applied Mathematics. 115. 349-355 (2000)

T.Kohno：“H 矩阵的迭代测试”计算与应用数学杂志。

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)

H.Niki：“预条件高斯-赛德尔方法”2000 年第 16 届 IMACS 世界大会科学计算、应用数学和模拟论文集。

K.Ojiro: ""A new direct test for H-matrix""Information. (to appear).

K.Ojiro：“H 矩阵的新直接测试”信息。