Numerical experiments in computing bounds for the norm of the error in the preconditioned conjugate gradient algorithm
Numerical experiments in computing bounds for the norm of the error in the preconditioned conjugate gradient algorithm
复制标题
预条件共轭梯度算法中误差范数计算界限的数值实验
DOI：
10.1023/a:1019179412560
复制
发表时间：
1999
影响因子：
2.1
通讯作者：
G. Meurant
中科院分区：
文献类型：
--
作者：
G. Meurant
在本文中，我们考虑了计算预处理共轭梯度（PCG）算法中误差 A-norm 的边界的算法。我们扩展了早先论文[8]中给出的 PCG 公式。我们给出的数值实验表明，只要给出或自适应计算出预处理矩阵的最小和最大特征值的估计值，就能得到很好的上下限。
In this paper we consider algorithms to compute bounds of the A-norm of the error in the preconditioned conjugate gradient (PCG) algorithm. We extend to PCG formulas that were given in an earlier paper [8]. We give numerical experiments which show that good upper and lower bounds can be obtained provided estimates of the lowest and largest eigenvalues of the preconditioned matrix are given or adaptively computed.