梯度神经网络解线性矩阵方程之收敛性分析

Convergence Analysis of Gradient Neural Network Solving Linear Matrix Equations

为了求解线性矩阵方程问题,应用一种基于负梯度法的递归神经网络模型,并探讨了该递归神经网络实时求解线性矩阵方程的全局指数收敛问题。在讨论渐近收敛性基础上,进一步证明了该类神经网络在系数矩阵满足有解条件的情况下具有全局指数收敛性,在不能满足有解条件的情况下具有全局稳定性。计算机仿真结果证实了相关理论分析和该网络实时求解线性矩阵方程的有效性。

To solve the problem of linear matrix equations, a type of negative-gradient based recurrent neural network is applied, and its global exponential convergence is investigated for the online solution. Base on the discussion of asymptotical convergence, global ex- ponential convergence （when the coefficients satisfy a unique-solution condition） and global stability （when the coefficients do not satis- fy such a condition） of GNN are proved further. Computer-simulation results substantiate the related theoretical analysis and efficacy of the neural network on solving online linear matrix equations.