The inspiration of the study concerns an iterative predictor-corrector method with order of convergence p=45 for computing the inverse of the coefficient matrix Λ=In⊗A+BT⊗Im, which is obtained by the Sylvester equation AX+XB=C. The numerical solutions of three examples by predictor-corrector algorithm are given. The final numerical results also support the applicability, fast convergency, and high accuracy of the method for finding matrix inverses
