The generalized reflexive and anti-reflexive matrices have several applications in engineering and scientific computations. In the present paper, first we propose a conjugate direction (CD) algorithm for finding the generalized reflexive solution X and the generalized anti-reflexive solution Y of the coupled Sylvester matrix equations
Then, we analyze the convergence properties of the CD algorithm under some plausible assumptions. Finally by applying two numerical examples, we compare the proposed algorithm with other popular iterative solvers in use today.
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