The optimal perturbation bounds of the Moore–Penrose inverse under the Frobenius norm

By Lingsheng Meng, Bing Zheng. 2010

48 citations recorded by the source corpus.

Abstract We obtain the optimal perturbation bounds of the Moore–Penrose inverse under the Frobenius norm by using Singular Value Decomposition, which improved the results in the earlier paper [P.-A. Wedin, Perturbation theory for pseudo-inverses, BIT 13 (1973) 217–232]. In addition, a perturbation bound of the Moore–Penrose inverse under the Frobenius norm in the case of the multiplicative perturbation model is also given.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/792c0a0d564577691e6e0175bd923a5eaffd5445

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In Computational Theory and Mathematics

1. David P. Woodruff
2. Anima Anandkumar
3. Samet Oymak
4. Alessandro Lazaric
5. Kamyar Azizzadenesheli
6. Necmiye Ozay
7. Jakub Konecný
8. Nicolas Loizou

In Numerical Analysis

1. David P. Woodruff
2. Anima Anandkumar
3. Samet Oymak
4. Kamyar Azizzadenesheli

Citations in the corpus

• Non-asymptotic Identification of LTI Systems from a Single Trajectory (2018, background): “First, pseudo-inverse satisfies the perturbation bound [20,30] We need to bound the right hand side.”
• Learning Two Layer Rectified Neural Networks in Polynomial Time (2018, background): “1 Meng and Zheng (2010)) Let B† denote the MoorePenrose Pseudoinverse of B, and let ‖B‖2 denote the operator norm of B.”
• Reinforcement Learning of POMDPs using Spectral Methods (2016, background): “W and Ŵ be any pair of matrix such that Ŵ = W + E for a suitable error matrix E, then we have Meng and Zheng (2010)”