梯度神经网络在求解矩阵平方根中的应用

摘要

Matrix square root problem can be regarded as a special case of matrix problems,and has a wide application in scientific and engineering fields.Different from the conventional numerical methods,the gradient neural network is adopted to solve matrix square root problem.In order to solve the square root of a matrix,a norm-based scalar-valued energy function is defined.Then,according to the graclient descent method,an evolution formula is designed.Thus,the gradient neural network is derived for finding the square root of a matrix by expanding the evolution formula.With the aid of computer simulation based on MATLAB,the simulation results confirm the accuracy and validity of the gradient neural network for finding matrix square root.Furthermore,by choosing different values of the design parameter,the convergence streed of the gradient neural network for matrix square root solving has been improved greatly.The results show that design parameter plays an important role in the gradient neural network for solving matrix square root.%矩阵的平方根问题是关于求解矩阵问题的一种特殊情况,在科学与工程领域中应用是极其广泛的.不同于用数值方法求解,采用梯度神经网络对矩阵平方根问题进行求解.为了求解一般矩阵的平方根,定义了一个基于范数的标量取值的能量函数,然后根据梯度下降法,设计了一个演化公式,从而推导出了求解矩阵平方根的梯度神经网络模型.借助MATLAB进行计算机模拟仿真,仿真结果证实了梯度神经网络在求解矩阵平方根的可行性和有效性.而且,通过选取不同的设计参数取值,可以大大加快梯度神经网络求解矩阵平方根的收敛速度.结果说明,设计参数的取值在梯度神经网络求解矩阵平方根当中有着至关重要的作用.