• THE PERTURBATION BOUNDS OF THE QR DECOMPOSITION OF MATRICES UNDER THE ADDITION PERTURBATION

Abstract

The perturbation bounds of the polar decomposition of matrices have been discussed by lots of scholars, such as the article , , . In this paper the methods in article will be extended, according to these methods the QR decomposition of matrices will be discussed when given an addition perturbation to them. In the QR decomposition of matrices the perturbation bounds will be given, which can realize on account of the properties of norm and the expression of ， ; the bounds will also be deduced by using the singular value decomposition of matrices.
Keywords: The QR decomposition; The singular value decomposition; Spectral norm; The perturbation bounds.