Perturbation bounds in connection with singular value decomposition
Perturbation bounds in connection with singular value decomposition
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DOI：
10.1007/bf01932678
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发表时间：
1972-03
影响因子：
1.5
通讯作者：
P. Wedin
中科院分区：
文献类型：
--
作者：
P. Wedin
LetAbe anm×n-matrix有点不安。在本文中，我们将推导出一个估计，在这种情况下，aha&ahh的不变子空间将受到多大的影响。对于Davis和Kahan[1]中的厄米线性算子，这些边界有sin（）定理作为特例。它们适用于超定线性方程组的计算解，尤其适用于用低秩矩阵代替秩亏的情况。
LetAbe anm×n-matrix which is slightly perturbed. In this paper we will derive an estimate of how much the invariant subspaces ofAHAandAAHwill then be affected. These bounds have the sin ϑ theorem for Hermitian linear operators in Davis and Kahan [1] as a special case. They are applicable to computational solution of overdetermined systems of linear equations and especially cover the rank deficient case when the matrix is replaced by one of lower rank.