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

作者：Kumar Ashim; Cardoso Joao R^*

来源：Applied Mathematics and Computation, 2018, 333: 246-253.

DOI：10.1016/j.amc.2018.03.078

• Yang-Baxter-like matrix equation
• Frechet derivative
• Iterative methods
• Convergence
• Stability
• Idempotent matrix

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.

• 出版日期2018-9-15