Table 4 Comparison between SALM and SSALM for \(p=0.3\)
From: A semi-smoothing augmented Lagrange multiplier algorithm for low-rank Toeplitz matrix completion
n | rank(M) | Algorithm | IT | time (s) | error 1 | error 2 |
|---|---|---|---|---|---|---|
500 | 10 | SALM | 46 | 11.3753 | 9.3029e−10 | 3.2509e−06 |
SSALM | 46 | 5.1926 | 6.5512e−10 | 1.8892e−08 | ||
800 | 10 | SALM | 57 | 17.3212 | 9.0562e−10 | 1.0264e−04 |
SSALM | 58 | 13.5300 | 5.7672e−10 | 1.9937e−05 | ||
1000 | 10 | SALM | 59 | 12.2900 | 9.8849e−10 | 2.9149e−07 |
SSALM | 58 | 7.9075 | 8.0278e−10 | 6.0819e−09 | ||
1500 | 10 | SALM | 69 | 38.0422 | 8.9932e−10 | 6.4286e−05 |
SSALM | 66 | 17.6928 | 5.5536e−10 | 4.7554e−08 | ||
2000 | 10 | SALM | 72 | 39.9752 | 9.1752e−10 | 3.8681e−07 |
SSALM | 70 | 30.0543 | 8.0322e−10 | 2.2090e−09 | ||
2500 | 10 | SALM | 78 | 92.3154 | 9.8020e−10 | 6.9561e−06 |
SSALM | 74 | 47.8242 | 9.2726e−10 | 6.3568e−09 | ||
3000 | 10 | SALM | 80 | 119.9347 | 8.6992e−10 | 6.7548e−06 |
SSALM | 80 | 84.1827 | 7.6381e−10 | 1.6034e−07 | ||
4000 | 20 | SALM | 74 | 187.0096 | 7.3863e−10 | 2.0127e−06 |
SSALM | 72 | 142.3911 | 8.5136e−10 | 3.0778e−08 | ||
5000 | 20 | SALM | 74 | 246.3862 | 9.4517e−10 | 4.4710e−07 |
SSALM | 78 | 219.6853 | 6.8201e−10 | 2.8025e−06 | ||
8000 | 25 | SALM | 83 | 1.4409e+03 | 9.9003e−10 | 2.7735e−04 |
SSALM | 84 | 1.1312e+03 | 8.0522e−10 | 3.7995e−04 |