From Zhang Neural Network to Newton Iteration for Matrix Inversion
From Zhang Neural Network to Newton Iteration for Matrix Inversion
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DOI：
10.1109/tcsi.2008.2007065
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发表时间：
2009-07
期刊：
影响因子：
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通讯作者：
Yunong Zhang;Weimu Ma;Binghuang Cai
中科院分区：
文献类型：
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作者：
Yunong Zhang;Weimu Ma;Binghuang Cai
与基于梯度的神经网络不同，张最近提出了一种特殊的递归神经网络（RNN）用于在线矩阵求逆。这种RNN是基于矩阵值误差函数而非标量值误差函数设计的。此外，它是用隐式动力学而非显式动力学来描述的。在本文中，我们开发并研究了张神经网络的离散时间模型（为表述方便如此称呼并缩写为ZNN），它由一组差分方程来描述。与用于矩阵求逆的牛顿迭代法相比，我们发现离散时间ZNN模型将牛顿迭代作为其特殊情况包含在内。注意到这种关系，我们对使用ZNN和牛顿迭代进行矩阵求逆的不同情况进行了数值比较。为了使ZNN具有更好的收敛性和稳定性，我们检验了不同种类的激活函数和不同的步长值。数值例子证明了ZNN和牛顿迭代在在线矩阵求逆方面的有效性。
Different from gradient-based neural networks, a special kind of recurrent neural network (RNN) has recently been proposed by Zhang for online matrix inversion. Such an RNN is designed based on a matrix-valued error function instead of a scalar-valued error function. In addition, it was depicted in an implicit dynamics instead of an explicit dynamics. In this paper, we develop and investigate a discrete-time model of Zhang neural network (termed as such and abbreviated as ZNN for presentation convenience), which is depicted by a system of difference equations. Comparing with Newton iteration for matrix inversion, we find that the discrete-time ZNN model incorporates Newton iteration as its special case. Noticing this relation, we perform numerical comparisons on different situations of using ZNN and Newton iteration for matrix inversion. Different kinds of activation functions and different step-size values are examined for superior convergence and better stability of ZNN. Numerical examples demonstrate the efficacy of both ZNN and Newton iteration for online matrix inversion.