关于PCG迭代矩阵特征值近似计算  

NUMERICAL COMPUTATON FOR EXTREME EIGENVALES OF THE PCG ITERATIVE MATRIX

作　　者：茹向阳[1] 雷光耀[1] 

机构地区：[1]中科院应用数学研究所,北京100080

出　　处：《计算物理》1992年第4期445-447,共3页Chinese Journal of Computational Physics

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

关 键 词：特征值 三对角矩阵 PCG 

分 类 号：O241.6[理学—计算数学]