Neural Processing Letters

, Volume 50, Issue 2, pp 1993–2005 | Cite as

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

  • Xuanjiao Lv
  • Lin Xiao
  • Zhiguo TanEmail author
  • Zhi Yang
  • Junying Yuan


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.


Gradient neural network Moore–Penrose inverse Global convergence Parallel-computation 



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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Nanfang College of Sun Yat-Sen UniversityGuangzhouChina
  2. 2.College of Information Science and EngineeringHunan UniversityChangshaChina
  3. 3.College of Information Science and EngineeringJishou UniversityJishouChina
  4. 4.School of Automation Science and EngineeringSouth China University of TechnologyGuangzhouChina

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