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中文摘要：
梯度算法广泛应用于训练前馈神经网络．对于单输出前馈神经网络的梯度算法的收敛性已经有了详细的讨论．研究了带有多个输出单元的BP神经网络的梯度算法，证明了误差函数在梯度算法所生成的权向量序列上的单调递减性，并且证明了梯度算法的弱收敛性和强收敛性．
英文摘要：
Gradient algorithm has been widely used for training the weights of feedforward neural networks. The convergence of the gradient algorithm for feedforward neural networks with one output unit has thoroughly studied. The convergence of gradient algorithm for a three - layer BP neural network with multiple output units is studied. The weak and strong convergence results of the corresponding gradient algorithm and the monotonicity of the error function in the iteration weighted vectors are proved.
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