矩阵求逆的一种神经网络方法

A Neural Network Method to Find the Inverse of a Matrix

科学计算中有很大一部分可以归结为矩阵计算，而矩阵计算的困难在于求逆。在矩阵退化或病态情况下，求逆就更困难。另一方面，非方矩阵逆有多种定义，使矩阵求逆更为复杂。因此，寻求一种新的能适应各种矩阵的求逆方法引起了人们的注意。作者提出一种基于ＢＰ算法的神经网络矩阵求逆方法。它适应面广，能避开病态数据，具有足够的求逆精度。

Most scientific calculations can be resolved to matrix calculations. One of the problem of matrix calculation is to solve the finding of an inverse of a matrix. When a matrix is singular or ill-conditioned the finding of the inverse of the matrix becomes more difficult on the other hand, it will be more complex because there are a lot of definitions of an inverse of a nonsquare matrix. Therefore, it is necessary to look for a new method to find the inverse of any given matrix. In this paper, based on BP algorithm, a neural network method is proposed to find the inverse of a matrix. The method can be used for either a nonsingular matrix, an ill-conditioned matrix or a nonsquare matrix with enough accuracy.