Iterative methods for finding commuting solutions of the Yang-Baxter-like matrix equation

摘要

The main goal of this paper is the numerical computation of solutions of the so-called Yang-Baxter-like matrix equation AXA=XAX, where A is a given complex square matrix. Two novel matrix iterations are proposed, both having second-order convergence. A sign modification in one of the iterations gives rise to a third matrix iteration. Strategies for finding starting approximations are discussed as well as a technique for estimating the relative error. One of the methods involves a very small cost per iteration and is shown to be stable. Numerical experiments are carried out to illustrate the effectiveness of the new methods. (C) 2018 Elsevier Inc. All rights reserved.