TY - JOUR
T1 - Perturbation Bounds for the Polar Factors
AU - Chen , Yuan
AU - Sun , Ji-Guang
JO - Journal of Computational Mathematics
VL - 4
SP - 397
EP - 401
PY - 1989
DA - 1989/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/9489.html
KW - 
AB - <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>