New perturbation bounds for the subunitary polar factors

Abstract

In this article, we present some new perturbation bounds for the (subunitary) unitary polar factors of the (generalized) polar decompositions. Two numerical examples are given to show the rationality and superiority of our results, respectively. In terms of the one-to-one correspondence between the weighted case and the non-weighted case, all these bounds can be applied to the weighted polar decomposition.

Keywords:

• polar decomposition
• perturbation bound
• weighted polar decomposition
• subunitary polar factor
• weighted unitary polar factor

AMS Subject Classifications::

• 15A09
• 15A18
• 15A45
• 65F35

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (No. 11171361) and in part by the Natural Science Foundation Project of CQ CSTC (No. 2010BB9215). The authors thank the anonymous referee and the editor for their valuable comments and suggestions for improving the quality of this article.