左端预处理Householder-GMRES(m)算法  

Left pretreatment Householder-GMRES(m) algorithm

作　　者：闫涛红 宋慧[1] 于春肖[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《辽宁工程技术大学学报（自然科学版）》2014年第8期1136-1140,共5页Journal of Liaoning Technical University (Natural Science)

基　　金：河北省自然科学基金资助项目(A2011203020);河北省高等学校科学技术研究重点基金资助项目(ZD2010116)

摘　　要：为解决大型稀疏矩阵的求解问题,采用一种改进的交替方向隐式方法和SSOR法提出两种不同的预处理器,并对Householder-GMRES(m)算法进行左端预处理,形成两种新算法,对算法的收敛性进行分析,给出数值算例验证新算法的可行性,同时对算法的计算精度和效率进行比较,得出有关影响因子.研究结果表明:提出的新算法计算精度和效率较好,在求解计算速度上具有优势和实用性,在实际计算中起到关键性的作用.In order to solve the problem of getting solution to large sparse matrix, this paper utilized an improved alternating direction implicit method and the SSOR method, obtained two kinds of different preprocessor, and left pretreatment for Householder - GMRES （m） algorithm, and created two new algorithms. By analyzing the convergence of the algorithm, the feasibility of the new algorithm is demonstrated through a numerical example, the calculation accuracy and efficiency of the algorithm is compared, and the impact factor is obtained . The results show that the calculation accuracy and efficiency of the algorithm put forward is well, and it has advantages in the calculation speed of solving problems and it is practica!, which will play a key role in the calculation of actual problems.

关 键 词：ADI法 SSOR法 预处理 计算精度 计算效率 

分 类 号：O241.6[理学—计算数学]