多项式函数型回归神经网络模型及应用

文中利用回归神经网络既有前馈通路又有反馈通路的特点，将网络隐层中神经元的激活函数设置为可调多项式函数序列，提出了多项式函数型回归神经网络新模型，它不但具有传统回归神经网络的特点，而且具有较强的函数逼近能力，针对递归计算问题，提出了多项式函数型回归神经网络学习算法，并将该网络模型应用于多元多项式近似因式分解，其学习算法在多元多项式近似分解中体现了较强的优越性，通过算例分析表明，该算法十分有效，收敛速度快，计算精度高，可适用于递归计算问题领域，该文所提出的多项式函数型回归神经网络模型及学习算法对于代数符号近似计算有重要的指导意义。

Polynomial Function Recurrent Neural Networks Model and Apply

A kind of polynomial function recurrent neural network (PFRNN) model is firstly proposed, which has characteristic of traditional RNN and the capability of function approximate. PFRNN is especially useful for recurrent computation problem. The PFRNN learning algorithm is also designed, which can perform approximate factorization of multivariate polynomials. This model has the properties such as easily trained and simply structured. However, the numbers of the hidden layer activation function are based on this model of the orders of the factorized polynomials. Finally, several examples and learning algorithm show that the proposed model is effective and practical. The learning algorithm is convergent quickly and stable, which can approximately calculate every polynomial factor. The results obtained in this paper are very important for study algebra symbolic approximate computation.