Volume 7, Issue 4
Perturbation Bounds for the Polar Factors

Chun-hui Chen & Ji-guang Sun

DOI:

J. Comp. Math., 7 (1989), pp. 397-401

Published online: 1989-07

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  • 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 $\|\tilde{H}-H\|_F\leq \sqrt{2}\|A^+\| \|\tilde{A}-A\|_F$ 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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@Article{JCM-7-397, author = {}, title = {Perturbation Bounds for the Polar Factors}, journal = {Journal of Computational Mathematics}, year = {1989}, volume = {7}, number = {4}, pages = {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 $\|\tilde{H}-H\|_F\leq \sqrt{2}\|A^+\| \|\tilde{A}-A\|_F$ hold, where $A^+$ is the Moore-Penrose inverse of A, and $\| \|_2$ and $\| \|_F$ denote the spectral norm and the Frobenius norm, respectively. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9489.html} }
TY - JOUR T1 - Perturbation Bounds for the Polar Factors 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 - 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 $\|\tilde{H}-H\|_F\leq \sqrt{2}\|A^+\| \|\tilde{A}-A\|_F$ hold, where $A^+$ is the Moore-Penrose inverse of A, and $\| \|_2$ and $\| \|_F$ denote the spectral norm and the Frobenius norm, respectively.
Chun-hui Chen & Ji-guang Sun. (1970). Perturbation Bounds for the Polar Factors. Journal of Computational Mathematics. 7 (4). 397-401. doi:
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