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Perturbation Analysis of the Moore-Penrose Inverse and the Weighted Moore-Penrose Inverse

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Generalized Inverses: Theory and Computations

Part of the book series: Developments in Mathematics ((DEVM,volume 53))

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Abstract

Let A be a given matrix. When computing a generalized inverse of A, due to rounding error, we actually obtain the generalized inverse of a perturbed matrix \(B=A+E\) of A. It is natural to ask if the generalized inverse of B is close to that of A when the perturbation E is sufficiently small.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, China

    Guorong Wang

  2. Department of Mathematics, Fudan University, Shanghai, China

    Yimin Wei

  3. Department of Computing and Software, McMaster University, Hamilton, ON, Canada

    Sanzheng Qiao

Authors
  1. Guorong Wang
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  2. Yimin Wei
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  3. Sanzheng Qiao
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Correspondence to Guorong Wang .

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Wang, G., Wei, Y., Qiao, S. (2018). Perturbation Analysis of the Moore-Penrose Inverse and the Weighted Moore-Penrose Inverse. In: Generalized Inverses: Theory and Computations. Developments in Mathematics, vol 53. Springer, Singapore. https://doi.org/10.1007/978-981-13-0146-9_8

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