摘要
对于预处理共轭梯度法,本文给出其迭代矩阵AM^(-1)与三对角阵B_s之间的关系,并对B_s的特征值分布作了分析,进而得到关于AM^(-1)特征值的一些性质。通过算例对两者的特征值及条件数进行了探讨。
This paper discusses the relationship between the iterative matrix AM ' of the preconditioned conjugate gradient (PCG) and the tridiagonal matrix B, obtained when the PCG iteration terminates. The distribution of eigenvalues of Bs is analysed and, consequently, several properties of eigenvalues of the PCG iterative matrix AM-1 are revealed. The numerical resuly shows that the simple and convenient method discussed here can be adopted to give a satisfying a pproximation to the
出处
《计算物理》
CSCD
北大核心
1992年第4期445-447,共3页
Chinese Journal of Computational Physics
关键词
特征值
三对角矩阵
PCG
preconditioned conjugate gradient, tridiagonal matrix, eigenvalue extreme eigenva