一种求解线性方程组的预处理方法

An Incomplete Decomposition for Solving Linear System

研究了一种基于不完全Crout分解的预处理方法。通过对VanderVorst构造的不完全分解LEQDEQUEQ加以改进，从而得到新的矩阵分解。可以证明，当系数矩阵A是非奇异M-矩阵和L-矩阵时，这种分解是对矩阵A进行的正则分裂。据此建立的求解方程组的迭代公式收敛。数值试验结果表明，这种预处理方法能够有效地提高迭代法的收敛速度。

Presents an preconditioning method which based on incomplete Crout decomPOsition.Through modifing the preconditioner LEPidUEQ established by Vander Vorst, a new splitting isobtained. We can prove that this splitting is a regular split of matrix A when A is a M-matrix orL-matrix. The algorithm established according to this splitting converges. Numerical experienceshows that this algorithm can improve the rate of convetgence effectively.