基于不同误差函数的神经网络求解线性方程组

Neural Network Based on Different Error Functions for Solving Linear System of Equations

对于同一线性方程,存在多种不同的求解方法,而且由于求解方法的不同,其收敛速度也存在差异.对一个一般的线性方程设计2个不同的误差函数,利用梯度下降法建立2个梯度神经网络模型.借助Matlab仿真软件进行计算机仿真,根据不同的梯度神经网络模型求出线性方程的解,从而证实2个梯度神经网络模型的可行性.最后借助Matlab软件模拟利用2个梯度神经网络模型求解线性方程时的收敛情况,比较2个梯度神经网络求解线性方程的收敛速度.

There are many ways to solve a linear equation,and various solving methods will result in different convergence speeds.Two different error functions are designed for one linear equation,and then two gradient neural network models are established according to the gradient descent method.Matlab is used for computer simulation,the solutions of linear equation are given according to the different gradient neural network models,and the feasibility of these two gradient neural network models is confirmed.Finally,the convergence speeds in solving the linear equation are compared.