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Matrixwe的开发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高斯 - 塞德尔法的收敛性。此外，可以解决一个非基因主导矩阵，该基质无法应用迭代方法。另一方面，Kohno开发了其他类型的预处理矩阵，并获得了许多有效的结果。与ICCG方法相比，所提出的方法在迭代数字和CPU时间方面非常出色。（2）H-Matrix的标准的开发。H-Matrix对于通过迭代方法的代数方程的线性系统解决方案非常重要。但是H-Matrix没有标准。我们开发了迭代标准作为新标准。这种方法是我们的完全原创。但是，法官需要许多迭代数字到所有H-Matrix。为了征服这一故障，我们发现了新的迭代标准（3），我们为线性互补问题提供了新的错误界限，其中所涉及的矩阵是p-matrix。严格的误差界限的计算可以转变为p-matrix线性间隔系统。此外，对于涉及的矩阵是带有正对角的H矩阵，可以通过求解比Mathias-Pang误差绑定的方程式线性系统来找到误差绑定。