In this paper, by employing the Zhang neural network (ZNN) method, an effective continuous-time LU decomposition (CTLUD) model is firstly proposed, analyzed, and investigated for solving the time-varying LU decomposition problem. Then, for the convenience of digital hardware realization, this paper proposes three discrete-time models by using Euler, 4-instant Zhang et al. discretization (ZeaD), and 8-instant ZeaD formulas to discretize the proposed CTLUD model, respectively. Furthermore, the proposed models are used to perform the LU decomposition of three time-varying matrices with different dimensions. Results indicate that the proposed models are effective for solving the time-varying LU decomposition problem, and the 8-instant ZeaD LU decomposition model has the highest precision among the three discrete-time models.

中文翻译：

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ZNN方法和ZeaD公式求解时变LU分解的新模型

本文采用张神经网络（ZNN）方法，提出了一种有效的连续时间LU分解模型（CTLUD），并进行了分析和研究，以解决时变LU分解问题。然后，为方便数字硬件的实现，本文利用Euler，4-instant Zhang等人提出了三种离散时间模型。离散化（ZeaD）和8即时ZeaD公式来离散化建议的CTLUD模型。此外，所提出的模型被用于执行具有不同维度的三个时变矩阵的LU分解。结果表明，所提出的模型对于解决时变LU分解问题是有效的，并且8瞬时ZeaD LU分解模型在三个离散时间模型中具有最高的精度。