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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Numer. Linear Algebra Appl. 2008; 00:1–00 Prepared
using nlaauth.cls [Version:
2002/09/18 v1.02]
Perturbation bounds for weighted polar decomposition in
the
weighted unitarily invariant norm
Hu Yang1 and Hanyu Li
College of Mathematics and Physics, Chongqing
University, Chongqing 400030, People’s Republic of China.
SUMMARY
In this paper, by generalizing the ideas of the
(generalized) polar decomposition to the weighted polar
decomposition and the unitarily invariant norm to the
weighted unitarily invariant norm, we present some
perturbation bounds for the generalized positive polar
factor, generalized nonnegative polar factor, and weighted
unitary polar factor of the weighted polar decomposition
in the weighted unitarily invariant norm. These bounds
extend the corresponding recent results for the
(generalized) polar decomposition. In addition, we also give the
comparison between the two perturbation bounds for the
generalized positive polar factor obtained from two
different methods. Copyright c 2008 John Wiley &
Sons, Ltd.
KEY WORDS: weighted polar decomposition; generalized
positive polar factor; generalized nonnegative polar
factor; weighted unitary polar factor; weighted unitarily
invariant norm
Correspondence
to: Hanyu Li, College of Mathematics and Physics, Chongqing University,
Chongqing 400030, P.R. China.
Email: lihy.hy@gmail.com
Contract/grant sponsor: Publishing Arts Research Council;
contract/grant number: 98–1846389
Received
Copyright c 2008
John Wiley & Sons, Ltd. Revised
http://mc.manuscriptcentral.com/nla
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