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Recurrent neural network for computing the W-weighted Drazin inverse

Author

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  • Wang, Xue-Zhong
  • Ma, Haifeng
  • Stanimirović, Predrag S.

Abstract

Two gradient based recurrent neural networks (RNNs) for computing the W-weighted Drazin inverse of a real rectangular matrix are proposed and considered. Usage of the first RNN is limited by a specific constraint on the spectrum of a certain matrix. The second RNN is usable without restrictions. The stability of the recurrent neural networks as well as their convergence are considered. Numerical examples are given to show the efficiency of the proposed neural networks.

Suggested Citation

  • Wang, Xue-Zhong & Ma, Haifeng & Stanimirović, Predrag S., 2017. "Recurrent neural network for computing the W-weighted Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 300(C), pages 1-20.
    • Handle: RePEc:eee:apmaco:v:300:y:2017:i:c:p:1-20
    DOI: 10.1016/j.amc.2016.11.030
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    References listed on IDEAS

    as
    1. Hernández, A. & Lattanzi, M. & Thome, N., 2016. "On some new pre-orders defined by weighted Drazin inverses," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 108-116.
    2. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, September.
    3. Kyrchei, Ivan, 2015. "Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 453-465.
    4. Yimin Wei & Hebing Wu, 2001. "Challenging Problems on the Perturbation of Drazin Inverse," Annals of Operations Research, Springer, vol. 103(1), pages 371-378, March.
    5. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    6. Xia, Youshen & Zhang, Songchuan & Stanimirović, Predrag S., 2016. "Neural network for computing pseudoinverses and outer inverses of complex-valued matrices," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1107-1121.
    7. Hernández, A. & Lattanzi, M. & Thome, N., 2015. "Weighted binary relations involving the Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 215-223.
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    Cited by:

    1. Khosro Sayevand & Ahmad Pourdarvish & José A. Tenreiro Machado & Raziye Erfanifar, 2021. "On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus," Mathematics, MDPI, vol. 9(19), pages 1-23, October.
    2. Ma, Haifeng & Stanimirović, Predrag S., 2019. "Characterizations, approximation and perturbations of the core-EP inverse," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 404-417.
    3. Stanimirović, Predrag S. & Petković, Marko D. & Mosić, Dijana, 2022. "Exact solutions and convergence of gradient based dynamical systems for computing outer inverses," Applied Mathematics and Computation, Elsevier, vol. 412(C).

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