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Improved Gradient Neural Networks for Solving Moore–Penrose Inverse of Full-Rank Matrix

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Abstract

Being with parallel-computation nature and convenience of hardware implementation, linear gradient neural networks (LGNN) are widely used to solve large-scale online matrix-involved problems. In this paper, two improved GNN (IGNN) models, which are activated by nonlinear functions, are first developed and investigated for Moore-Penrose inverse of full-rank matrix. The global convergence performances of such two models and LGNN models are theoretically analyzed. Two illustrative examples are performed to further demonstrate the theoretical results as well as the feasibility and efficacy of the proposed IGNN models for solving full-rank matrix Moore-Penrose inverse in real time. At last, a robot application example is provided to show the practical utility of the proposed IGNN models.

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Authors and Affiliations

  1. Nanfang College of Sun Yat-Sen University, Guangzhou, 510970, China

    Xuanjiao Lv, Zhi Yang & Junying Yuan

  2. College of Information Science and Engineering, Hunan University, Changsha, 410082, China

    Lin Xiao

  3. College of Information Science and Engineering, Jishou University, Jishou, 416000, China

    Lin Xiao

  4. School of Automation Science and Engineering, South China University of Technology, Guangzhou, 510641, China

    Zhiguo Tan

Authors
  1. Xuanjiao Lv
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  2. Lin Xiao
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  3. Zhiguo Tan
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  4. Zhi Yang
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  5. Junying Yuan
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Correspondence to Zhiguo Tan.

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Lv, X., Xiao, L., Tan, Z. et al. Improved Gradient Neural Networks for Solving Moore–Penrose Inverse of Full-Rank Matrix. Neural Process Lett 50, 1993–2005 (2019). https://doi.org/10.1007/s11063-019-09983-x

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