Perturbation Bounds for the Polar Factors

Perturbation Bounds for the Polar Factors

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

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

Keywords:   

Author Details

Yuan Chen

Ji-Guang Sun