Numerical Solution of Sylvester Equation Based on Iterative Predictor-Corrector Method

Abstract

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 Lambda = (I-n circle times A) + (B-T circle times I-m), 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.