Table 3 Comparison between SALM and SSALM for \(p=0.4\)
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 | 45 | 7.8497 | 6.8884e−10 | 5.3595e−06 |
SSALM | 44 | 2.3892 | 5.3103e−10 | 2.3267e−09 | ||
800 | 10 | SALM | 54 | 7.4948 | 9.3427e−10 | 2.1464e−06 |
SSALM | 54 | 5.9618 | 8.9128e−10 | 1.5780e−08 | ||
1000 | 10 | SALM | 58 | 9.9528 | 9.7372e−10 | 3.2663e−05 |
SSALM | 56 | 7.2641 | 9.7968e−10 | 2.4662e−09 | ||
1500 | 10 | SALM | 67 | 25.3226 | 9.8741e−10 | 2.7106e−06 |
SSALM | 64 | 16.1484 | 9.0982e−10 | 1.5210e−09 | ||
2000 | 10 | SALM | 70 | 34.6083 | 8.4557e−10 | 1.8757e−07 |
SSALM | 70 | 29.7298 | 6.4346e−10 | 1.7874e−09 | ||
2500 | 10 | SALM | 76 | 54.5748 | 7.1288e−10 | 8.4514e−08 |
SSALM | 74 | 46.5716 | 4.9981e−10 | 1.6792e−09 | ||
3000 | 10 | SALM | 78 | 84.9121 | 5.3019e−10 | 2.2285e−06 |
SSALM | 76 | 66.0761 | 9.2876e−10 | 1.1697e−09 | ||
4000 | 20 | SALM | 73 | 164.7655 | 8.6946e−10 | 7.3598e−06 |
SSALM | 72 | 144.5329 | 5.1358e−10 | 1.4439e−09 | ||
5000 | 20 | SALM | 75 | 251.7641 | 8.9821e−10 | 7.9543e−08 |
SSALM | 76 | 203.3167 | 8.3168e−10 | 3.4049e−08 | ||
8000 | 25 | SALM | 79 | 598.8095 | 9.5617e−10 | 3.7230e−08 |
SSALM | 80 | 530.8533 | 4.9436e−10 | 1.2710e−09 |