针对BP算法收敛速度慢的问题 ,提出了多层前向神经网络的新型二阶递推学习算法 .给出了一种新的矩阵求逆引理 ,从Newton迭代法入手 ,推导出新型递推学习算法 .该算法等价于Newton迭代法并且有二阶收敛速度 ,能同时反向传播网络各层误差和二阶导数信息因子 ,还能实现Newton搜索方向和Hessian阵逆的递推运算 .基于微分方程稳定性理论 ,研究了新算法的全局收敛性 .分析表明 ,新算法优于BP算法并且具有全局收敛性 Aiming at the problem of slow convergence rate of BP algorithm, a new type of second-order recursive learning algorithm for multi-layer feedforward neural networks is proposed. A new matrix inversion lemma is given. Starting from the Newton iteration method, a new type of recursion Learning algorithm.The algorithm is equivalent to the Newton iteration method and has the second-order convergence rate, which can reverse the error and the second-order derivative information factor of the network at the same time, and can also realize the recursion of Newton search direction and Hessian matrix inverse. The stability of the differential equation theory, the global convergence of the new algorithm is studied. The analysis shows that the new algorithm is superior to the BP algorithm and has the global convergence