关于H-矩阵的H-预处理子（英文）  

H-Preconditioner for H-matrices

作　　者：刘仲云[1] 于静[1] 张艳[1] 张育林 

机构地区：[1]长沙理工大学数学与统计学院,湖南长沙410004 [2]Minho学数学中心,葡萄牙4710057

出　　处：《应用数学》2017年第1期144-150,共7页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China under Grant(11371075);the research innovation program of Hunan province of China for postgraduate students under Grant(CX2015B374)

摘　　要：设A为一实对称正定的严格对角占优矩阵.设A=D-B为A的Jacobi分裂.为了求解线性方程组Ax=b,在新提出的预处理子的基础上,我们采用预处理共轭梯度方法(PCG)来求解该问题.新提出的预处理子Pv=D+νvv^T,其中v=|B|e,e=(1,...,1)~T,ν=v^TBv/||v||_2~4,且ν使||cvv^T-B||_F达到极小.我们得到了预处理矩阵P_v^(-1)A特征值的上下界,它的界比JIN提出的预处理子的界简单紧凑.数值结果表明我们的预处理子的有效性.Let A be real symmetric positive definite and strictly diagonally dominant. Let A = D - B be the Jacobi splitting of A. We propose a new preconditioner in the form of P,, = D ＋ vvvT for solving the linear system Ax = b by the preconditioned conjugate gradient （PCG） method, where v is chosen to be v = ｜B｜e with e -- （1,..., 1）T and v = vTBv/｜｜v｜｜42 minimizing ｜｜cvvT - B｜｜E We obtain lower and upper bounds of the eigenvalues of preconditioned matrix Pv-1A, which are sharper and simpler than Jin＇s preconditioner. Numerical results demonstrate the effectiveness of our preconditioners.

关 键 词：严格对角占优矩阵 H矩阵 Jacobi分裂 预处理子 预处理共轭梯度方法(PCG) 

分 类 号：O241.63[理学—计算数学]