Abstract
It is well known that the upper bounds of the weighted Moore–Penrose inverse
play a fundamental role in the perturbation analysis for the weighted linear least squares problem. In this note, we provide a sharp estimation for
,
(1)
(1) Thus norm estimations for the weighted Moore–Penrose inverses of the acute perturbations can be improved uniformly.
Acknowledgments
The author would like to thank the editor and two referees for their detailed comments which greatly improve the presentation of the paper. Partially work was finished during the author visited at Nis University, the author thanks Professor Dragana S. Cvetković-Ilić for her great hospitality.
Disclosure statement
No potential conflict of interest was reported by the author.