# 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.

## Keywords

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

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