New results on the convergence of the conjugate gradient method
New results on the convergence of the conjugate gradient method
复制标题
共轭梯度法收敛的新结果
DOI：
10.1002/nla.618
复制
发表时间：
2009
影响因子：
4.3
通讯作者：
H. Sadok
中科院分区：
文献类型：
--
作者：
R. Bouyouli;G. Meurant;Laurent Smoch;H. Sadok
证明了求解正定对称线性方程组的共轭梯度法(CG)收敛的有关理论结果。在Sadok(Numer)的一些早期结果的基础上，考虑到矩阵逆的投影的逆，给出了误差的A范数与残差的范数之比的新的关系式。算法2005；40：201-216)。我们结果的证明依赖于CG方法和Lanczos算法之间众所周知的对应关系。版权所有©2008 John Wiley&Sons，Ltd.
This paper is concerned with proving theoretical results related to the convergence of the conjugate gradient (CG) method for solving positive definite symmetric linear systems. Considering the inverse of the projection of the inverse of the matrix, new relations for ratios of the A‐norm of the error and the norm of the residual are provided, starting from some earlier results of Sadok (Numer. Algorithms 2005; 40:201–216). The proofs of our results rely on the well‐known correspondence between the CG method and the Lanczos algorithm. Copyright © 2008 John Wiley & Sons, Ltd.