A Generalized HSS Iteration Method for Continuous Sylvester Equations

Table 1

Numerical results for GHSS and HSS with the experimental optimal iteration parameters.

𝑞	𝑛	Method
		GHSS				HSS
		𝛼1exp	𝛽1exp	IT	CPU	𝛼exp	IT	CPU
𝑞=0.01	𝑛=10	0.01	0.83	2	0.0006	1.66	12	0.0038
	𝑛=20	0.01	0.90	3	0.0018	0.80	23	0.0148
	𝑛=40	0.01	0.77	4	0.0141	0.42	43	0.1018
	𝑛=80	0.01	0.06	8	0.1038	0.24	85	0.9943
	𝑛=160	0.01	0.03	21	1.5376	0.14	169	11.605
𝑞=0.1	𝑛=10	0.03	1.00	4	0.0012	1.70	12	0.0036
	𝑛=20	0.01	0.95	4	0.0025	0.84	24	0.0151
	𝑛=40	0.01	0.61	6	0.0140	0.48	47	0.1102
	𝑛=80	0.01	0.21	11	0.1265	0.26	93	1.0787
	𝑛=160	0.01	0.10	24	1.6567	0.16	181	12.488
𝑞=1	𝑛=10	0.67	1.00	8	0.0025	1.82	13	0.0039
	𝑛=20	0.29	0.96	13	0.0081	0.98	23	0.0148
	𝑛=40	0.29	0.59	24	0.0563	0.62	35	0.0821
	𝑛=80	0.34	0.43	41	0.4750	0.46	50	0.5885
	𝑛=160	0.31	0.33	66	4.5142	0.34	70	4.7983
𝑞=10	𝑛=10	6.70	2.00	11	0.0034	1.88	12	0.0040
	𝑛=20	8.80	1.90	15	0.0097	1.16	21	0.0135
	𝑛=40	4.90	1.50	20	0.0477	0.68	37	0.0898
	𝑛=80	3.60	1.30	29	0.3395	0.90	57	0.6780
	𝑛=160	2.00	1.00	40	2.7869	0.68	83	5.8003
𝑞=100	𝑛=10	70.5	2.58	7	0.0021	1.72	12	0.0036
	𝑛=20	49.0	2.70	8	0.0052	0.90	20	0.0130
	𝑛=40	16.0	2.45	10	0.0243	0.48	36	0.0885
	𝑛=80	6.00	1.70	15	0.1782	0.28	64	0.7664
	𝑛=160	1.70	1.05	32	2.2333	0.16	110	7.6504