New additive perturbation bounds of the Moore-Penrose inverse

Abstract

In this paper, we obtain new additive perturbation bounds of the Moore-Penrose inverse under the unitarily invariant norm and the Q-norm by using the singular value decomposition, respectively. These bounds always improve the corresponding ones in [Cai L et al. Additive and multiplicative perturbation bounds for the Moore-Penrose inverse. Linear Algebra Appl. 2011;434:480–489].

Keywords:

• Moore-Penrose inverse
• singular value decomposition
• additive perturbation bound

AMS Subject Classifications:

• 15A09
• 15A24

Acknowledgments

We would like to express our sincere thanks to the anonymous reviewers for their valuable suggestions which greatly improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11701458].