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On the perturbation of the Moore–Penrose inverse of a matrix

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  • Xu, Xuefeng

Abstract

The Moore–Penrose inverse of a matrix has been extensively investigated and widely applied in many fields over the past decades. One reason for the interest is that the Moore–Penrose inverse can succinctly express some important geometric constructions in finite-dimensional spaces, such as the orthogonal projection onto a subspace and the linear least squares problem. In this paper, we establish new perturbation bounds for the Moore–Penrose inverse under the Frobenius norm, some of which are sharper than the existing ones.

Suggested Citation

  • Xu, Xuefeng, 2020. "On the perturbation of the Moore–Penrose inverse of a matrix," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    • Handle: RePEc:eee:apmaco:v:374:y:2020:i:c:s0096300319309129
    DOI: 10.1016/j.amc.2019.124920
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    References listed on IDEAS

    as
    1. Xu, Xuefeng, 2017. "Generalization of the Sherman–Morrison–Woodbury formula involving the Schur complement," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 183-191.
    2. Bodnar, Taras & Dette, Holger & Parolya, Nestor, 2016. "Spectral analysis of the Moore–Penrose inverse of a large dimensional sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 160-172.
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