@Article{JCM-7-4,
author = {Yuan, Chen and Sun, Ji-Guang},
title = {Perturbation Bounds for the Polar Factors},
journal = {Journal of Computational Mathematics},
year = {1989},
volume = {7},
number = {4},
pages = {397--401},
abstract = {<p style="text-align: justify;">Let $A$, $\tilde{A}\in C^{m\times n}$, rank (A)=rank ($\tilde{A}$)=$n$. Suppose that $A=QH$ and $\tilde{A}=\tilde{Q}\tilde{H}$ are the polar decompositions of $A$ and $\tilde{A}$, respectively. It is proved that $$\|\tilde{Q}-Q\|_F\leq 2\|A^+\|_2\|\tilde{A}-A\|_F$$ and $$\|\tilde{H}-H\|_F\leq \sqrt{2}\|\tilde{A}-A\|_F$$ hold, where $A^+$ is the Moore-Penrose inverse of $A$, and $\| \|_2$ and $\| \|_F$ denote the spectral norm and the Frobenius norm, respectively.</p>},
issn = {1991-7139},
doi = {https://doi.org/1989-JCM-9489},
url = {https://global-sci.com/article/86123/perturbation-bounds-for-the-polar-factors}
}