Some refined bounds for the perturbation of the orthogonal projection and the generalized inverse

被引：0
|
作者：
Wen Li
Yanmei Chen
Seakweng Vong
Qilun Luo
机构：
[1] South China Normal University,School of Mathematical Sciences
[2] Guangdong Polytechnic Normal University,School of Mathematics and Systems Science
[3] University of Macau,Department of Mathematics
来源：
Numerical Algorithms | 2018年 / 79卷
关键词：
Singular value decomposition; Orthogonal projection; Perturbation; Generalized inverse; 65F10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider the perturbation of the orthogonal projection and the generalized inverse for an n × n matrix A and present some perturbation bounds for the orthogonal projections on the rang spaces of A and A∗, respectively. A combined bound for the orthogonal projection on the rang spaces of A and A∗ is also given. The proposed bounds are sharper than the existing ones. From the combined bounds of the orthogonal projection on the rang spaces of A and A∗, we derived new perturbation bounds for the generalized inverse, which always improve the existing ones. The combined perturbation bound for the orthogonal projection and the generalized inverse is also given. Some numerical examples are given to show the advantage of the new bounds.
引用
收藏
页码：657 / 677
页数：20
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