NORM ESTIMATIONS FOR PERTURBATIONS OF THE WEIGHTED MOORE-PENROSE INVERSE
Xiaobo Zhang, Qingxiang Xu, Yimin Wei · Journal of Applied Analysis & Computation · 2016
For a complex matrix A ∈ Cm×n, the relationship between the weighted Moore-Penrose inverse AM1N1 and A M2N2 is studied, and an important formula is derived, where M1 ∈ Cm×m, N1 ∈ Cn×n and M2 ∈ Cm×m, N2 ∈ Cn×n are different pair of positive definite hermitian matrices. Based on this formula, this paper initiates the study of the perturbation estimations for AMN in the case that A is fixed, whereas both M and N are variable. The obtained norm upper bounds are then applied to the perturbation estimations for the solutions to the weighted linear least squares problems.