Abstract
Many works on solving matrix equations are related to the complex nonlinear Yang–Baxter matrix equation $$ AXA=XAX $$, where $$ A \in {\mathbb {C}}^{n \times n}$$ is a given matrix and X is an unknown matrix. The Yang–Baxter matrix equation has been widely studied by its application in various fields of mathematics and physics. In this paper, we introduce an iterative method based on the Hermitian and skew-Hermitian splitting of coefficient matrix A for solving complex nonlinear Yang–Baxter matrix equation. Then, we prove the convergence of the new scheme subject to some conditions. Finally, an example is solved to discover the applicability of the new method via comparing it with some related previous methods.
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