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Journal of Applied Mathematics
Volume 2012, Article ID 219025, 15 pages
http://dx.doi.org/10.1155/2012/219025
Research Article

Relative and Absolute Perturbation Bounds for Weighted Polar Decomposition

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received 21 October 2011; Accepted 20 December 2011

Academic Editor: Juan Manuel Peña

Copyright © 2012 Pingping Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some new perturbation bounds for both weighted unitary polar factors and generalized nonnegative polar factors of the weighted polar decompositions are presented without the restriction that A and its perturbed matrix A˜ have the same rank. These bounds improve the corresponding recent results.