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

Abstract

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.

Keywords

• reduced biquaternion
• e-extra iteration method
• complex decomposition
• convergence analysis
• numerical example