A Parallel Preconditioned Modified Conjugate Gradient Method for Large Sylvester Matrix Equation

Table 1

Numerical results of Example 7.

	𝑝	8	12	16	20
Parameter iterative method (𝛼=−0.3015)	𝑇 (s)	571.2402	411.2114	310.7856	251.4239
	𝐾	33	33	33	33
	𝐸1	0.53	0.49	0.48	0.48
	Δ	7.21𝑒−11	7.21𝑒−11	7.21𝑒−11	7.21𝑒−11
Parameter iterative method (𝛼=−0.4083)	𝑇 (s)	564.0080	394.3398	301.6541	246.2671
	𝐾	31	31	31	31
	𝐸1	0.53	0.51	0.50	0.49
	Δ	7.21𝑒−11	7.21𝑒−11	7.21𝑒−11	7.21𝑒−11
MCG algorithm	𝑇 (s)	641.1601	427.8546	332.7490	271.4428
	𝐾	79	79	79	79
	𝐸1	0.47	0.47	0.46	0.45
	Δ	9.80𝑒−11	9.80𝑒−11	9.80𝑒−11	9.80𝑒−11
The algorithm in the paper (𝛼=−0.3015)	𝑇 (s)	303.8564	220.1811	176.6607	151.9282
	𝐾	20	20	20	20
	𝐸1	1	0.92	0.86	0.80
	Δ	9.82𝑒−11	9.82𝑒−11	9.82𝑒−11	9.82𝑒−11
The algorithm in the paper (𝛼=−0.4083)	𝑇 (s)	301.6773	216.2561	167.5985	141.9657
	𝐾	18	18	18	18
	𝐸1	1	0.93	0.90	0.85
	Δ	6.39𝑒−11	6.39𝑒−11	6.39𝑒−11	6.39𝑒−11