【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.更多还原

【Abstract】 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 asymmetric positive definite but nonsingular linear algebraic equations,Firstly,giveing the technology of incomplete LU decomposition preprocessing matrix structure;Then,the SSOR preconditioning decomposition and its improved decomposition are proposed.And based on the ILUCG 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.更多还原