一个拟极小化左共轭梯度算法及其数值表现  

A QUASI-MINIMIZED LEFT CONJUGATE GRADIENT METHOD AND ITS NUMERICAL BEHAVIOR

作　　者：王丽平[1] 陈晓红[1] 

机构地区：[1]南京航空航天大学数学系,南京210016

出　　处：《计算数学》2009年第2期127-136,共10页Mathematica Numerica Sinica

摘　　要：左共轭梯度法是求解大型稀疏线性方程组的一种新兴的Krylov子空间方法.为克服该算法数值表现不稳定、迭代中断的缺点,本文对原方法进行等价变形,得到左共轭梯度方向的另一迭代格式,给出一个拟极小化左共轭梯度算法.数值结果证实了该变形算法与原算法的相关性.The left conjugate gradient method is a recently developed Krylov subspace method which aims to solve large-scale sparse linear systems. In order to overcome the drawbacks of numerical instability and possible breakdowns in the iteration, we transform the formula of the left conjugate gradient method into an equivalent version to generate the left conjugate gradient directions. And this technique is used to construct a quasi-minimized left conju- gate gradient method. The numerical results reported in this paper confirm the correlation between this equivalent algorithm and the left conjugate gradient method.

关 键 词：迭代法 左共轭梯度法 左共轭梯度方向 拟极小化 

分 类 号：O241.6[理学—计算数学]