Iterative methods based on low-rank matrix for solving the Yang–Baxter-like matrix equation

We propose an effective matrix iteration method and a novel zeroing neural network (NZNN) model for finding numerical commuting solutions of the (time-invariant) Yang–Baxter-like matrix equation in this paper. The proposed matrix iteration method has a second-order convergence speed, and it is proved to be stable. How to proceed with initial value selection and termination criteria are discussed. Meanwhile, two numerical experiments are adopted to illustrate the superiority of the proposed matrix iteration method in computational efficiency. The NZNN model based on Tikhonov regularization for solving the time-invariant Yang–Baxter-like matrix equation is given. Besides, numerical results are provided to substantiate the efficiency, availability and superiority of the developed NZNN model for time-invariant Yang–Baxter-like matrix equation problems.