基于Hessian矩阵的模糊优选BP算法及其应用

在模糊优选神经网络理论的基础上，提出了等效误差函数的概念。建立了基于误差函数的Hessian矩阵的一种BP算法。该方法应用数值计算方法中的Newton迭代法显著提高了计算中的学习效率。将该方法应用于大连市经济、水资源和环境规划的决策分析中，取得了满意的效果。

Back propagation learning algorithm with Hessian matrix for fuzzy optimal neural networks

On the basis of theory for fuzzy optimal neural networks, the concept of equivalent error function is introduced to establish a new back propagation learning (BP) algorithm with Hessian matrix to promote the calculation. The Newton's iteration method is applied to promote the training efficiency and accelerate the convergence. This method is used to calculate the decision-making analysis for economy, water resources and environment planning of the Dalian City.