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

Algorithm 1

Predictor-corrector algorithm

	Choose an initial matrix under the assumption where .
	Step 1. Let . Evaluate and ; then, calculate .
	Do Step 2–Step 6 until .
	Step 2. Evaluate .
	Step 3. Apply , the predictor step of the predictor-corrector method (11), to find .
	Step 4. Evaluate .
	Step 5. Apply , the corrector step of the predictor-corrector method (11), to find .
	Step 6. Evaluate and , respectively. Then, calculate .
	Let .
	Step 7. If is the performed iteration number, then the approximate solution is that satisfies .