New algorithms to compute the nearness symmetric solution of the matrix equation

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Table 1 Iteration time (seconds) and iteration numbers for four methods

m, n, p	Algorithm 1		Algorithm 2		Algorithm CG		Algorithm LSQR
m, n, p	IT	CPU	IT	CPU	IT	CPU	IT	CPU
20, 20, 20	2807	1.0407	1992	0.9338	941	0.1603	816	0.1181
40, 40, 40	6709	60.3186	5085	52.1359	3445	25.3471	2925	21.6702
60, 60, 60	8109	74.2018	7882	67.0493	7203	45.1428	5987	43.2527
80, 80, 80	8246	88.6394	5503	73.6081	10,974	88.6511	9773	83.7413
100, 80, 80	5795	67.6304	2081	23.6263	6681	59.9316	5636	54.6361
200, 80, 80	9445	130.5067	2503	12.2904	4721	60.9609	4913	55.7173
400, 80, 60	13,756	252.4951	2234	0.2925	1885	22.5552	1518	20.8768
80, 80, 100	2843	46.9736	6082	82.7429	7393	66.6155	6228	59.0029
80, 80, 200	728	8.8492	7324	101.4176	4768	62.8689	4855	54.1167
60, 80, 400	25	0.4173	14,009	258.8992	2245	40.7279	1786	22.5928
100, 80, 100	332	3.9936	352	4.1774	2011	18.5992	1604	16.1305
200, 80, 200	39	0.7021	38	0.6241	531	7.8664	459	6.9108
200, 80, 400	21	0.5096	41	0.9568	299	11.5416	348	7.3581
400, 80, 200	41	1.0451	22	0.4941	415	8.7829	361	7.8676