An efficient iterative algorithm for finding a nontrivial symmetric solution of the Yang-Baxter-like matrix equation

This paper presents an efficient iterative method to obtain a nontrivial symmetric solution of the Yang-Baxter-like matrix equation A X A = X A X . Necessary conditions for the convergence of the propounded iterative method are derived. Finally, three numerical examples to illustrate the efficiency of the proposed method and the preciseness of our theoretical results are provided.