This paper intends to solve the time-varying Yang-Baxter-like matrix equation (TVYBLME), which is frequently employed in the fields of scientific computing and engineering applications. Due to its critical and promising role, several methods have been constructed to generate a high-performing solution for the TVYBLME. However, given the fact that noise is ubiquitous and inevitable in actual systems. It is necessary to design a computational algorithm with strong robustness to solve the TVYBLME, which has rarely been mentioned previously. For this reason, to remedy shortcomings that the conventional computing methods have encountered in a noisy case, a modified Newton integration (MNI) neural algorithm is proposed and employed to solve the TVYBLME. In addition, the related theoretical analyses show that the proposed MNI neural algorithm has the noise-tolerance ability under various noisy cases. Finally, the feasibility and superiority of the proposed MNI neural algorithm to solve the TVYBLME are verified by simulation experiments.

本文旨在求解在科学计算和工程应用领域中经常使用的时变类杨-巴克斯特矩阵方程 (TVYBLME)。由于其关键和有前途的作用，已经构建了几种方法来为 TVYBLME 生成高性能解决方案。然而，鉴于噪声在实际系统中无处不在且不可避免。需要设计一种鲁棒性强的计算算法来解决TVYBLME，这在以前很少被提及。为此，为了弥补传统计算方法在噪声情况下遇到的缺点，提出并采用改进的牛顿积分（MNI）神经算法来解决TVYBLME。此外，相关理论分析表明，所提出的MNI神经算法在各种噪声情况下均具有抗噪声能力。最后通过仿真实验验证了所提出的MNI神经算法求解TVYBLME的可行性和优越性。