基于改进BP算法的广义逆矩阵求解方法

A Method to Find Generalized Inverse Matrix on the Basis of Improved BP Algorithm

:研究了广义逆矩阵的人工神经网络求解.基于改进的BP算法,提出了求解广义逆的3层网络的拓扑结构,包括各层神经元的个数、排列方式,提出了各层之间连接权值的分布规则等,推导出了求解15类广义逆所必需的4个计算公式.程序模拟证明,这种方法可以求出包括方阵、长方阵和病态矩阵在内的所有类型矩阵的广义逆矩阵.

This paper studies a method to find generalized inverse matrix on the basis of ANN. Based on improved BP algorithm, the topology of the 3layer network able to find generalized inverse matrix is designed, including the number of each layer's neurons, the way how they should be arranged, and the arrangement rule of weights between layers, etc. Also the 4 necessary formulas are deduced to find the solution of 15 kinds of generalized inverse matrix. The computer program simulation proves that by means of this method, generalized inverse matrix of all kinds of matrix including square, rectangle or morbid ones can be found.