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Perturbation bounds of generalized inverses

Author

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  • Meng, Lingsheng
  • Zheng, Bing
  • Ma, Peilan

Abstract

Let complex matrices A and B have the same sizes. We characterize the generalized inverse matrix B(1, i), called an {1, i}-inverse of B for each i=3 and 4, such that the distance between a given {1, i}-inverse of a matrix A and the set of all {1, i}-inverses of the matrix B reaches minimum under 2-norm (spectral norm) and Frobenius norm. Similar problems are also studied for {1, 2, i}-inverse. In practice, the matrix B is often considered as the perturbed matrix of A, and hence based on the previous results, the additive perturbation bounds for the {1, i}- and {1, 2, i}-inverses and multiplicative perturbation bounds for the {1}-, {1, i}- and {1, 2, i}-inverses are proposed. Numerical examples show that these multiplicative perturbation bounds can be achieved respective under 2-norm and Frobenius norm.

Suggested Citation

  • Meng, Lingsheng & Zheng, Bing & Ma, Peilan, 2017. "Perturbation bounds of generalized inverses," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 88-100.
    • Handle: RePEc:eee:apmaco:v:296:y:2017:i:c:p:88-100
    DOI: 10.1016/j.amc.2016.10.017
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    Cited by:

    1. Quach, Sara & Jebarajakirthy, Charles & Thaichon, Park, 2017. "Aesthetic labor and visible diversity: The role in retailing service encounters," Journal of Retailing and Consumer Services, Elsevier, vol. 38(C), pages 34-43.

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