UNITARILY INVARIANT NORM AND <i>Q</i>-NORM ESTIMATIONS FOR THE MOORE–PENROSE INVERSE OF MULTIPLICATIVE PERTURBATIONS OF MATRICES

Juan Luo

doi:10.11948/20190206

2020 Volume 10 Issue 3

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Juan Luo. UNITARILY INVARIANT NORM AND Q-NORM ESTIMATIONS FOR THE MOORE–PENROSE INVERSE OF MULTIPLICATIVE PERTURBATIONS OF MATRICES[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 1107-1117. doi: 10.11948/20190206

Citation:

Juan Luo. UNITARILY INVARIANT NORM AND Q-NORM ESTIMATIONS FOR THE MOORE–PENROSE INVERSE OF MULTIPLICATIVE PERTURBATIONS OF MATRICES[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 1107-1117. doi: 10.11948/20190206

UNITARILY INVARIANT NORM AND Q-NORM ESTIMATIONS FOR THE MOORE–PENROSE INVERSE OF MULTIPLICATIVE PERTURBATIONS OF MATRICES

Juan Luo^1, ,

1.
Department of Mathematics, Shanghai Normal University, 100 Guilin Rd., 200234 Shanghai, China

Corresponding author: Email address:luojuan@shnu.edu.cn(J. Luo)

Abstract

Abstract

Let $B$ be a multiplicative perturbation of $A\in\mathbb{C}^{m\times n}$ given by $B = D_1^* A D_2$, where $D_1\in\mathbb{C}^{m\times m}$ and $D_2\in\mathbb{C}^{n\times n}$ are both nonsingular. New upper bounds for $\Vert B^\dagger-A^\dagger\Vert_U$ and $\Vert B^\dagger-A^\dagger\Vert_Q$ are derived, where $A^\dagger,B^\dagger$ are the Moore-Penrose inverses of $A$ and $B$, and $\Vert \cdot\Vert_U,\Vert \cdot\Vert_Q$ are any unitarily invariant norm and $Q$-norm, respectively. Numerical examples are provided to illustrate the sharpness of the obtained upper bounds.
- Moore-Penorse inverse /
- multiplicative perturbation /
- unitarily invariant norm /
- Q-norm /
- norm upper bound
MSC: 34E10, 60H10, 92B05, 92D25

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References

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