A Finite Iterative Algorithm for Calculating a Hermitian Solution to a Single‐Variable Generalized Quaternion Matrix Equation

ABSTRACT A quaternion matrix is called Hermitian (self‐adjoint) if This study provides a finite iterative algorithm for determining a Hermitian solution to a single‐variable generalized quaternion matrix equation. Assuming consistency, the technique converges to a solution in a finite number of steps from any initial matrix, independent of round‐off errors. Some lemmas and a principal theorem are investigated to build the theoretical foundation of this method. As an application of the proposed equation, we present an algorithm for finding a Hermitian solution to a quaternion matrix equation, which includes ‐conjugate of the unknown quaternion matrix for some Numerical examples are provided to substantiate the efficacy of the established algorithm. These algorithms can be performed in MATLAB software through the QTFM toolbox.