用新激活函数加快新ZNN模型求解时变矩阵Moore-Penrose逆
Accelerating the New ZNN Model to Solve the Moore-Penrose Inverse of Time-Varying Matrix by Using a New Activation Function
DOI: 10.12677/PM.2024.141002, PDF,    国家自然科学基金支持
作者: 唐智超, 高月凤*：上海理工大学理学院，上海
关键词: Moore-Penrose逆；张神经网络；激活函数；时变矩阵；Moore-Penrose Inverse； Zhang Neural Network； Activation Function； Time-Varying Matrix
摘要: 基于梯度的神经网络(GNN)和张神经网络(ZNN)是两种可用于求解时变矩阵Moore-Penrose逆问题的递归神经网络。与GNN相比，ZNN的计算精度更高。此外，本文提出了一种新的ZNN模型。因此，本文主要利用带有新优化激活函数的ZNN模型来求解时变行满秩(或列满秩)矩阵Moore-Penrose逆问题。这种带有新优化激活函数的ZNN模型可以在有限时间内加速求解时变矩阵的Moore-Penrose逆。通过Lyapunov理论分析，得到了收敛时间的上限。仿真结果进一步证实了理论分析，并证明了采用新优化的激活函数的ZNN模型在求解时变矩阵Moore-Penrose逆时的有效性。
Abstract: Gradient-based neural networks (GNN) and Zhang neural networks (ZNN) are two types of recurrent neural networks that can be used to solve online time-varying matrix Moore-Penrose inverse problems. Compared with GNN, ZNN has higher computational accuracy. Moreover, a new ZNN model is proposed in this paper. Therefore, this paper focuses on solving the online time-varying full row-rank (or full column-rank) matrix Moore-Penrose inverse by using ZNN models with newly optimized activation functions. This ZNN model with the newly optimized activation functions can accelerate the Moore-Penrose inverse of time-varying matrices in finite time. An upper bound on the convergence time is obtained by Lyapunov theoretical analysis. Simulation results further confirm the theoretical analysis and demonstrate the effectiveness of the ZNN model with the newly optimized activation functions for solving time-varying matrix Moore-Penrose inverse.
文章引用：唐智超, 高月凤. 用新激活函数加快新ZNN模型求解时变矩阵Moore-Penrose逆[J]. 理论数学, 2024, 14(1): 9-16. https://doi.org/10.12677/PM.2024.141002

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