| Volume 6, Number 1, 2016, Pages 216-226 DOI：10.11948/2016018 |
| Norm estimations for perturbations of the weighted Moore-Penrose inverse |
| XiaoboZhang,Qingxiang Xu,Yinmin Wei |
| Keywords:Weighted Moore-Penrose inverse norm upper bound weighted linear least squares problem. |
| Abstract: |
| For a complex matrix $A\in \mathbb{C}^{m\times n}$, the relationship between the weighted Moore-Penrose inverse $A^\dag_{M_1N_1}$ and $A^\dag_{M_2N_2}$ is studied, and an important formula is derived,where $M_1\in \mathbb{C}^{m\times m}, N_1\in\mathbb{C}^{n\times n}$ and $M_2\in \mathbb{C}^{m\times m}, N_2\in\mathbb{C}^{n\times n}$ are different pair of positive definite hermitian matrices. Based on this formula, this paper initiates the study of the perturbation
estimations for $A^\dag_{MN}$ 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. |
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