(R, S) conjugate solution to coupled Sylvester complex matrix equations with conjugate of two unknowns

In this work, we are concerned with (R, S) - conjugate solutions to coupled Sylvester complex matrix equations with conjugate of two unknowns. When the considered two matrix equations are consistent, it is demonstrated that the solutions can be obtained by utilizing this iterative algorithm for any initial arbitrary (R, S) - conjugate matrices V-1, W-1 . A necessary and sufficient condition is established to guarantee that the proposed method converges to the (R, S) - conjugate solutions. Finally, two numerical examples are provided to demonstrate the efficiency of the described iterative technique.

Automated summary

In this research, we focus on finding solutions to coupled Sylvester complex matrix equations with conjugates of two unknowns. An iterative algorithm is used to obtain the solutions when the matrix equations are consistent. A condition is established to ensure the convergence of the proposed method. Numerical examples are provided to demonstrate the efficiency of the described iterative technique.