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Gradient Neural Network with Nonlinear Activation for Computing Inner Inverses and the Drazin Inverse

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Abstract

Two gradient-based recurrent neural networks (GNNs) for solving two matrix equations are presented and investigated. These GNNs can be used for generating various inner inverses, including the Moore–Penrose, and in the computation of the Drazin inverse. Convergence properties of defined GNNs are considered. Certain conditions which impose convergence towards the pseudoinverse, and the Drazin inverse are exactly specified. The influence of nonlinear activation functions on the convergence performance of defined GNN models is investigated. Computer simulation experience further confirms the theoretical results.

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Acknowledgements

The author would like to thank the editor and three referees for their detailed comments which greatly improved the presentation of the paper.

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia

    Predrag S. Stanimirović & Marko D. Petković

  2. Aristoteleion Panepistimion, Thessalonikis, Greece

    Dimitrios Gerontitis

Authors
  1. Predrag S. Stanimirović
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  2. Marko D. Petković
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  3. Dimitrios Gerontitis
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Corresponding author

Correspondence to Predrag S. Stanimirović.

Additional information

Predrag S. Stanimirović and Marko D. Petković gratefully acknowledge the support from Research Project 174013 of the Serbian Ministry of Science.

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Stanimirović, P.S., Petković, M.D. & Gerontitis, D. Gradient Neural Network with Nonlinear Activation for Computing Inner Inverses and the Drazin Inverse. Neural Process Lett 48, 109–133 (2018). https://doi.org/10.1007/s11063-017-9705-4

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