梯度神经网络求解Sylvester方程之MATLAB仿真

MATLAB Simulation of Gradient-based Neural Network for Sylvester Equation Solving

近年来,国内外学者发表了许多关于线性代数问题实时求解的方法,其中包括了矩阵求逆和线性方程组的并行求解方法。在研究了基于梯度法的递归神经网络用于Sylvester矩阵方程的实时求解后,通过使用Kronecker乘积和矩阵向量化等技术进行了MATLAB仿真从而验证了相关理论分析。计算机仿真的结果证实了这类神经网络方法在解决Sylvester矩阵方程中的有效性和高效率(特别是在使用幂S型激励函数的情况下)。

In recent years, many studies have been reported on real-time solution of algebraic problems including matrix inversion and linear equations solving. After a gradient-based recurrent neural network being investigated for the real-time solution of Sylvester matrix equation, its MATLAB simulation was conducted, where the Kronecker product and vectorization techniques were employed. Computer-simulation results substantiate the theoretical analysis and efficacy of such a neural network on Sylvester equation solving, especially when power-sigmoid activation functions are used.