梯度下降神经网络方法求解雅可比矩阵奇异的非线性方程组

Solving Nonlinear Equations with Singular Jacobi Matrix Based on Gradient Descend Neural Network

给出了一种雅可比矩阵奇异的非线性方程组的求解方法,通过把非线性方程组转化为一个无约束优化问题,采用梯度下降神经网络求解。对于唯一根的非线性方程组,该方法能够收敛到其唯一根;对于具有多个根的非线性方程组,该方法能够找到尽可能多的根。并且,该方法无需计算非线性方程组的雅克比矩阵,适用范围广。

A method is presented for nonlinear equations with singular Jacobi matrix.After transforming nonlinear equations into an unconstrained optimization problem,the nonlinear equations can be solved by gradient descend neural network model.For nonlinear equations with unique root,this method can converge to its unique root;and for nonlinear equations with several roots,this method can find the roots as many as possible.In addition,the method is widely used in application without calculation of Jacobi matrix.