An E-extra iteration method for solving reduced biquaternion matrix equation $ AX+XB = C $

Abstract

<abstract><p>This paper focuses on the solution of the reduced biquaternion equation $ AX+XB = C $ using the E-extra iteration method. By utilizing the complex decomposition of a reduced biquaternion matrix, we transform the equation into a complex matrix equation. Subsequently, we analyze the convergence of this method and provide guidelines for selecting optimal parameters. Finally, numerical examples are presented to demonstrate the efficacy of our algorithm.</p></abstract>