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

Journal of Inequalities and Applications

Table 2 Comparison between SALM and SSALM for \(p=0.5\)

n	rank(M)	Algorithm	IT	time (s)	error 1	error 2
500	10	SALM	44	2.8955	9.5801e−10	2.2756e−08
500	10	SSALM	44	2.1933	4.4278e−10	2.3334e−09
800	10	SALM	56	8.6741	7.0000e−10	2.6659e−06
800	10	SSALM	52	5.4772	9.2740e−10	3.3480e−09
1000	10	SALM	60	11.0450	8.2993e−10	6.6858e−08
1000	10	SSALM	56	6.7779	8.6651e−10	1.8478e−09
1500	10	SALM	68	20.6328	8.45398e−10	9.6939e−07
1500	10	SSALM	64	15.6997	9.3584e−10	1.5261e−09
2000	10	SALM	71	44.8591	9.9033e−10	7.2479e−08
2000	10	SSALM	68	27.9845	9.6632e−10	2.8679e−09
2500	10	SALM	78	67.4042	7.3828e−10	1.2312e−07
2500	10	SSALM	74	45.3268	7.1109e−10	2.5905e−09
3000	10	SALM	77	74.2323	7.2763e−10	9.9884e−09
3000	10	SSALM	76	64.4300	8.2104e−10	1.2376e−08
4000	20	SALM	73	155.9955	9.4452e−10	1.8879e−06
4000	20	SSALM	72	128.0443	7.1470e−10	1.8278e−09
5000	20	SALM	74	235.1514	9.1421e−10	7.9369e−06
5000	20	SSALM	76	200.7122	6.2859e−10	3.5799e−09
8000	25	SALM	80	622.5518	9.5065e−10	5.5408e−06
8000	25	SSALM	80	498.8602	5.1021e−10	3.0270e−08