A semi-smoothing augmented Lagrange multiplier algorithm for low-rank Toeplitz matrix completion

Journal of Inequalities and Applications

Table 1 Comparison between SALM and SSALM for \(p=0.6\)

n	rank(M)	Algorithm	IT	time (s)	error 1	error 2
500	10	SALM	44	2.6563	8.2372e−10	1.0363e−07
500	10	SSALM	42	1.8853	9.2608e−10	1.9658e−09
800	10	SALM	54	5.9456	8.1138e−10	8.2779e−09
800	10	SSALM	52	5.0976	5.6384e−10	7.6367e−09
1000	10	SALM	57	8.2474	8.9636e−10	4.1947e−09
1000	10	SSALM	58	6.3207	7.9333e−10	1.9217e−09
1500	10	SALM	64	16.7198	9.5636e−10	2.1154e−09
1500	10	SSALM	64	15.0399	9.1550e−10	1.0551e−09
2000	10	SALM	71	31.7924	9.4056e−10	7.5879e−08
2000	10	SSALM	68	26.8256	8.1847e−10	2.3201e−08
2500	10	SALM	71	47.3399	7.0194e−10	1.5048e−08
2500	10	SSALM	72	42.5214	9.8809e−10	2.6892e−09
3000	10	SALM	77	70.2107	6.7658e−10	2.4626e−09
3000	10	SSALM	76	60.6145	6.9232e−10	1.1348e−09
4000	20	SALM	74	146.3660	6.5154e−10	5.1684e−05
4000	20	SSALM	72	129.2216	5.3346e−10	1.4304e−09
5000	20	SALM	74	220.6386	9.9475e−10	2.1943e−08
5000	20	SSALM	74	198.3210	5.5006e−10	1.8351e−09
8000	25	SALM	78	550.5427	9.2197e−10	3.6735e−09
8000	25	SSALM	80	471.4695	5.5647e−10	1.5932e−09