@Article{JCM-4-245,
author = {Jian-Qin Mao},
title = {The Perturbation Analysis of the Product of Singular Vector Matrices $UV^T$},
journal = {Journal of Computational Mathematics},
year = {1986},
volume = {4},
number = {3},
pages = {245--248},
abstract = {<p style="text-align: justify;">Let A be an $n\times n$ nonsingular real matrix, which has singular value decomposition $A=U\sum V^T$. Assume A is perturbed to $\tilde{A}$ and $\tilde{A}$ has singular value decomposition $\tilde{A}=\tilde{U}\tilde{\sum}\tilde{V}^T$. It is proved that $\|\tilde{U}\tilde{V}^T-UV^T\|_F\leq \frac{2}{\sigma_n}\|\tilde{A}-A\|_F$, where $\sigma_n$ is the minimum singular value of A; $\|\dot\|_F$ denotes the Frobenius norm and $n$ is the dimension of A. <br/>This inequality is applicable to the computational error estimation of orthogonalization of a matrix, especially in the strapdown inertial navigation system.</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/9585.html}
}