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

Wen, Ruiping; Li, Shuzhen; Duan, Yonghong

doi:10.1186/s13660-019-2033-7

Journal of Inequalities and Applications

Table 6 Comparison between SALM and SSALM for \(\ell =3\)

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

n	rank(M)	p	Algorithm	IT	time (s)	error 1	error 2	RATIO (%)
500	10	0.4	SALM	47	7.5689	5.2053e−10	3.9970e−06	71.71
500	10	0.4	SSALM	47	5.4276	3.8663e−10	3.2564e−06	71.71
1000	10	0.4	SALM	60	13.9741	8.8726e−10	2.6235e−07	61.58
1000	10	0.4	SSALM	59	8.6048	9.8580e−10	9.1642e−09	61.58
1500	10	0.5	SALM	68	29.6545	9.1634e−10	4.5666e−05	63.99
1500	10	0.5	SSALM	68	18.9748	8.6885e−10	4.3619e−09	63.99
1500	10	0.3	SALM	69	47.1327	9.3547e−10	6.8306e−06	65.78
1500	10	0.3	SSALM	68	31.0025	9.0834e−10	2.2110e−06	65.78
2000	10	0.5	SALM	73	50.5371	8.4794e−10	3.1914e−05	59.00
2000	10	0.5	SSALM	71	29.8151	9.8594e−10	8.2954e−09	59.00
2000	10	0.4	SALM	72	38.5308	6.6310e−10	9.5342e−07	75.51
2000	10	0.4	SSALM	69	29.0941	9.3350e−10	3.5384e−09	75.51
3000	10	0.5	SALM	79	83.3712	9.9293e−10	1.2756e−05	76.68
3000	10	0.5	SSALM	78	63.9294	6.5972e−10	2.8985e−09	76.68
3000	10	0.4	SALM	77	80.7144	8.9678e−10	2.0862e−07	83.38
3000	10	0.4	SSALM	78	67.2993	9.9493e−10	7.3612e−09	83.38
3000	10	0.3	SALM	79	118.3675	9.8435e−10	9.6348e−05	81.24
3000	10	0.3	SSALM	80	96.1642	7.0585e−10	1.4254e−06	81.24
4000	20	0.6	SALM	73	152.4618	8.2869e−10	1.7109e−06	75.89
4000	20	0.6	SSALM	72	115.7083	8.2721e−10	2.4255e−09	75.89
4000	20	0.5	SALM	72	166.5827	9.3233e−10	1.0321e−07	74.92
4000	20	0.5	SSALM	72	124.8054	7.5040e−10	2.4066e−09	74.92
4000	20	0.4	SALM	75	186.7383	9.0624e−10	7.5345e−07	73.03
4000	20	0.4	SSALM	74	136.3765	8.7658e−10	1.0216e−07	73.03
5000	20	0.5	SALM	75	232.0879	9.8661e−10	5.7423e−08	80.86
5000	20	0.5	SSALM	75	187.6559	9.6715e−10	2.2527e−08	80.86
5000	20	0.4	SALM	76	250.9495	8.5572e−10	1.1830e−06	83.20
5000	20	0.4	SSALM	77	208.7798	9.7333e−10	7.8349e−07	83.20
5000	20	0.3	SALM	76	273.7735	9.4519e−10	6.4327e−06	86.76
5000	20	0.3	SSALM	80	237.5358	5.0062e−10	8.2082e−06	86.76
8000	25	0.5	SALM	80	575.2382	9.1308e−10	5.0447e−05	82.81
8000	25	0.5	SSALM	81	476.3530	7.4764e−10	4.6774e−08	82.81
8000	25	0.4	SALM	80	512.3396	9.7395e−10	6.3150e−06	97.00
8000	25	0.4	SSALM	81	496.9932	7.2501e−10	9.3571e−09	97.00
8000	25	0.3	SALM	83	579.2973	7.1372e−10	1.3349e−06	90.08
8000	25	0.3	SSALM	80	521.8350	9.4433e−10	6.5484e−09	90.08

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