Year: 1989
Author: Yuan Chen, Ji-Guang Sun
Journal of Computational Mathematics, Vol. 7 (1989), Iss. 4 : pp. 397–401
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1989-JCM-9489
Journal of Computational Mathematics, Vol. 7 (1989), Iss. 4 : pp. 397–401
Published online: 1989-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 5