求解线性方程组的两种不完全分解法

Two Incomplete Decomposition Methods for Solving large Sparse Unsymmetric Linear System

不完全分解方法常应用于求解大型稀疏非对称线性方程组。本文利用修正Gram-Schmidt过程对线性方程组系数矩阵给出了两种不完全分解,即不完全正交分解(ILQ)与不完全三角分解(ILU)的方法,数值试验结果表明,用这种分解预处理线性方程组,可有效地提高求解线性方程组的迭代敛速。

Incomplete decomposition methods are of often considered for the large and sparse unsymmetric linear system of equations. By Gram-Schmidt progress,the incomplete LQ decomposition and incomplete LU decomposition are obtained. These two methods are all applied to solve linear systems and their convergence behaviours are well demonstrated by numerical experiments.