A finite iterative algorithm for solving a single-variable quaternion system of matrix equations

Abstract

This paper introduces a finite iterative algorithm for solving a single-variable quaternion system of matrix equations. It is theoretically proven that if the system is consistent, the solution can be achieved from any initial quaternion matrix within a finite number of iterations, assuming the absence of round-off errors. A special case of this equation is studied, which contains the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="bold-italic">k</mml:mi> </mml:mrow> </mml:math> -conjugate of the unknown matrix. Numerical examples are provided to illustrate the effectiveness and computational efficiency of the proposed algorithms.