新预处理ILUCG法求解稀疏病态线性方程组  

NEW PRECONDITIONING ILUCG METHOD FOR SOLVING SPARSE ILL-CONDITIONED LINEAR EQUATIONS

作　　者：于春肖[1] 苑润浩[1] 穆运峰[2] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004 [2]燕山大学信息科学与工程学院,河北秦皇岛066004

出　　处：《数值计算与计算机应用》2014年第1期21-27,共7页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金项目(11301459);河北省自然科学基金项目(A2011203020);秦皇岛市科学技术研究与发展计划项目(2012021A046)

摘　　要：大型稀疏病态线性方程组的高效求解在科学计算和工程应用中起着十分重要的作用.对于一般非对称正定的非奇异线性代数方程组,首先介绍常用的不完全LU分解预处理矩阵构造技术;然后给出SSOR预处理分解及其改进分解,并基于ILUCG思想提出新预处理ILUCG法同时给出收敛性分析;最后进行数值模拟仿真试验,数值结果表明该算法是有效可行的,且较之一般的预处理ILUCG方法该法在求解稀疏病态方程组方面具有优越性.The efficient solution of the large sparse ill-conditioned linear equations plays a very important role in scientific computing and engineering applications. For the generally asym- metric positive definite but nonsingular linear algebraic equations, Firstly, giveing the tech- nology of incomplete LU decomposition preprocessing matrix structure ; Then , the SSOR preconditioning decomposition and its improved decomposition are proposed . And based on the ILUCC method, the new preconditioning ILUCG algorithm is presented; Finally, by numerical experiments, the numerical results show that the iterative algorithm is effective and feasible , and comparing with general preconditioning ILUCG methods, the proposed algorithm is quite superior.

关 键 词：稀疏病态线性方程组 预处理技术 不完全因子分解 ILUCG方法 

分 类 号：O241.6[理学—计算数学]