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

非对角占优矩阵基本迭代方法的综合研究。

基本信息

批准号：
15540144
负责人：
NIKI Hiroshi
金额：
$ 2.3万
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：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540144/
关键词：
accuracy H-matrix preconditioning the iterative method finite difference the CG method Kryllov su space method NCP function

项目摘要

(1)Development of the new preconditioning matrixWe 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.

(1)新的预处理矩阵的开发我们开发了新的预处理矩阵。使用新的预处理矩阵可以加速经典Gauss-Seidel方法的收敛。此外，还可以求解无法应用迭代方法的非对角主导矩阵。另一方面，Kohno开发了其他类型的预处理矩阵并取得了许多有效的结果。与ICCG方法相比，该方法在迭代次数和CPU时间上都有优势。(2)H矩阵判据的开发。H矩阵对于用迭代方法求解线性代数方程组非常重要。但H矩阵没有标准。我们开发了迭代准则作为新准则。这个方法是我们完全原创的。然而，对所有H矩阵的判断需要很多迭代次数。为了克服这个错误，我们发现了新的迭代准则（3）我们为所涉及的矩阵是P矩阵的线性互补问题给出了新的误差界限。严格误差界的计算可以转化为P矩阵线性区间系统。此外，对于所涉及的矩阵是具有正对角线的H矩阵，可以通过求解比Mathias-Pang误差界更尖锐的线性方程组来找到误差界。