Topics in matrix analysis
Analog VLSI and neural systems
Analog VLSI and neural systems
A Systolic Architecture for Fast Dense Matrix Inversion
IEEE Transactions on Computers
A recurrent neural network for real-time matrix inversion
Applied Mathematics and Computation
A recurrent neural network for solving Sylvester equation with time-varying coefficients
IEEE Transactions on Neural Networks
Design and analysis of a general recurrent neural network model for time-varying matrix inversion
IEEE Transactions on Neural Networks
Multi-dimensional Capon spectral estimation using discrete Zhang neural networks
Multidimensional Systems and Signal Processing
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This paper investigates the simulation of a gradient-based recurrent neural network for online solution of the matrix-inverse problem. Several important techniques are employed as follows to simulate such a neural system. 1) Kronecker product of matrices is introduced to transform a matrix-differential-equation (MDE) to a vector-differential-equation (VDE); i.e., finally, a standard ordinary-differential-equation (ODE) is obtained. 2) MATLAB routine "ode45" is introduced to solve the transformed initial-value ODE problem. 3) In addition to various implementation errors, different kinds of activation functions are simulated to show the characteristics of such a neural network. Simulation results substantiate the theoretical analysis and efficacy of the gradient-based neural network for online constant matrix inversion.