关键词: 不定方程, BP神经网络, Hopfield神经网络, 学习同质性

Abstract: The online solution of underdetermined linear equations is investigated by using two types of artificial neural networks (ie., BP and Hopfieldtype neural networks). Although they differ from each other in terms of origins, network definition, structures and learning patterns, the BP and Hopfieldtype neural networks could be exploited for solving online such underdetermined linear equations and even possess a common mathematical formulation of learning and common computational abilities. In addition, based on zero initial values, the same but nonzero initial values and different random initial values, computersimulation and verification results are given. These substantiate well the efficacy and commonness of such two types of neural networks on solving underdetermined linear equations.

Key words: underdetermined equation, BP neural network, Hopfield neural network, common nature of learning