Global exponential convergence and stability of gradient-based neural network for online matrix inversion

作者：Zhang, Yunong^*; Shi, Yanyan; Chen, Ke; Wang, Chaoli

来源：Applied Mathematics and Computation, 2009, 215(3): 1301-1306.

DOI：10.1016/j.amc.2009.06.048

• Gradient-based neural network
• Online matrix inversion
• Lyapunov stability theory
• Asymptotical convergence
• Global exponential convergence

Wang proposed a gradient-based neural network (GNN) to solve online matrix-inverses. Global asymptotical convergence was shown for such a neural network when applied to inverting nonsingular matrices. As compared to the previously-presented asymptotical convergence, this paper investigates more desirable properties of the gradient-based neural network; e. g., global exponential convergence for nonsingular matrix inversion, and global stability even for the singular-matrix case. Illustrative simulation results further demonstrate the theoretical analysis of gradient-based neural network for online matrix inversion.

• 出版日期2009-10
• 单位上海理工大学; 中山大学