基于前向和中间差分的离散ZNN的定常矩阵求逆方法

Constant matrix inversion method of discrete-time ZNN based on forward-difference and central-difference

不同于传统的梯度神经网络,一类特殊的用于解决时变问题(如时变矩阵求逆)的新型递归神经网络(ZNN)于2001年提出.为了便于使用数字电路进行硬件实现,需要将该类递归神经网络进行离散化,在之前工作的基础上,利用多点前向差分和中间差分数值微分方法,得到一类通过一系列ZNN离散模型表示的矩阵求逆方法,数学分析结果表明,传统牛顿迭代法可以看作其中一个特例.为验证此方法的有效性,针对定常矩阵求逆问题进行求解,同时,利用线搜索算法来保证该模型的收敛速度.实验结果表明,基于多种数值微分公式并辅以线搜索算法的ZNN离散模型可以较好地收敛到问题的理论解,且具有较佳的收敛性能.

A special class of recurrent neural networks（ZNN）,different from the conventional gradient-based neural network,were proposed in 2001 for solving time-varying problems（e.g.time-varying matrix inversion）.For possible digital-circuit realization,such ZNN models need to be discretized.Based on the previous work,a method depicted by a series of discrete-time ZNN（DTZNN） models was proposed for matrix inversion by exploiting multiple-point forward-difference and central-difference formulas.Mathematical analysis shows that Newton iteration is actually a special case of DTZNN models.In order to verify the efficacy of the DTZNN models,these models are applied for constant matrix inversion.In addition,a line-search algorithm is employed to guarantee the convergence of such DTZNN models.Results show that the discrete-time ZNN models based on difference formulas and aided with line-search algorithm are effective on constant matrix inversion and have superior convergent performance.