Norm estimations for perturbations of the weighted Moore-Penrose inverse |
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Authors: | XiaoboZhang Qingxiang Xu Yinmin Wei |
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Affiliation: | Department of Mathematics, Shanghai Normal University, Shanghai 200234,PR China,Department of Mathematics, Shanghai Normal University, Shanghai 200235,PR China and Institute of Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, 200433, PR China |
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Abstract: | For a complex matrix $Ain mathbb{C}^{mtimes n}$, 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 $M_1in mathbb{C}^{mtimes m}, N_1inmathbb{C}^{ntimes n}$ and $M_2in mathbb{C}^{mtimes m}, N_2inmathbb{C}^{ntimes n}$ are different pair of positive definite hermitian matrices. Based on this formula, this paper initiates the study of the perturbationestimations 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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Keywords: | Weighted Moore-Penrose inverse norm upper bound weighted linear least squares problem. |
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