NORM ESTIMATIONS FOR PERTURBATIONS OF THE WEIGHTED MOORE-PENROSE INVERSE

Xiaobo Zhang; Qingxiang Xu; Yimin Wei

doi:10.11948/2016018

2016 Volume 6 Issue 1

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Xiaobo Zhang, Qingxiang Xu, Yimin Wei. NORM ESTIMATIONS FOR PERTURBATIONS OF THE WEIGHTED MOORE-PENROSE INVERSE[J]. Journal of Applied Analysis & Computation, 2016, 6(1): 216-226. doi: 10.11948/2016018

Citation:

Xiaobo Zhang, Qingxiang Xu, Yimin Wei. NORM ESTIMATIONS FOR PERTURBATIONS OF THE WEIGHTED MOORE-PENROSE INVERSE[J]. Journal of Applied Analysis & Computation, 2016, 6(1): 216-226. doi: 10.11948/2016018

NORM ESTIMATIONS FOR PERTURBATIONS OF THE WEIGHTED MOORE-PENROSE INVERSE

1 Department of Mathematics, Shanghai Normal University, Shanghai 200234, PR China;
2 Institute of Mathematics, School of Mathematical Sciences, Fudan University, Shanghai, 200433, PR China

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Abstract

Abstract

For a complex matrix A ∈ C^m×n, the relationship between the weighted Moore-Penrose inverse A_M1N1 and A _M2N2 is studied, and an important formula is derived, where M₁ ∈ C^m×m, N₁ ∈ C^n×n and M₂ ∈ C^m×m, N₂ ∈ C^n×n are different pair of positive definite hermitian matrices. Based on this formula, this paper initiates the study of the perturbation estimations for A_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.
- Weighted Moore-Penrose inverse /
- norm upper bound /
- weighted linear least squares problem
MSC: 15A09;15A60;65F35

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References

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