We investigate solutions to the system of linear equations (SoLE) in both the time-varying and time-invariant cases, using both gradient neural network (GNN) and Zhang neural network (ZNN) designs. Two major limitations should be overcome. The first limitation is the inapplicability of GNN models in time-varying environment, while the second constraint is the possibility of using the ZNN design only under the presence of invertible coefficient matrix. In this paper, by overcoming the possible limitations, we suggest, in all possible cases, a suitable solution for a consistent or inconsistent linear system. Convergence properties are investigated as well as exact solutions.

我们同时使用梯度神经网络（GNN）和张神经网络（ZNN）设计研究时变和时不变情况下线性方程组（SoLE）的解决方案。应该克服两个主要限制。第一个限制是GNN模型在时变环境中的不适用性，而第二个限制是仅在存在可逆系数矩阵的情况下才可以使用ZNN设计。在本文中，通过克服可能的限制，我们建议在所有可能的情况下，为一致或不一致的线性系统提供合适的解决方案。研究收敛性质以及精确解。