Gradient-Based Neural Network for Solving Linear Matrix Equations and its MATLAB Simulative Verification

A gradient-based Hopfield-type neural network was investigated for the online solution of linear matrix equation.In addition to theoretical analysis of such a neural-network model,several important MATLAB simulation techniques are employed.Kronecker product of matrices is introduced to transform a matrix-form differential equation(MDE) to a vector-form differential equation(VDE);then,a standard ordinary-differential-equation(ODE) is obtained.MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem.In addition to various implementation errors,different kinds of activation-function array are coded to show the characteristics of such a gradient-based neural network.Simulation results substantiate the theoretical analysis and efficacy of the proposed gradient-based neural network for solving online the linear matrix equation(LME) problem.