In this study, first we derive a novel iteration scheme for the sign of a matrix with no pure imaginary eigenvalues. The fourth-order convergence speed of this scheme is given in detail. Secondly, we extend the obtained results so as to calculate the solution of the Yang-Baxterlike equation for the matrix A with no pure imaginary eigenvalues. Some numerical tests are also furnished to manifest the applicability of our method. Keywords Yang-Baxter-like • Matrix sign function • Convergence analysis • Iteration scheme • Eigenvalues Mathematics Subject Classification 65F60 • 15A24 wherein both A and X are square matrices of similar dimensions is called the Yang-Baxterlike equation (shorthanded as Y-B-like), see e.g., Ding and Rhee (2015), Dong and Ding (2016). This is mainly because of its similarity to the classical equation of Yang-Baxter, Communicated by Jinyun Yuan.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.