From: Multistep schemes for solving backward stochastic differential equations on GPU
K | N | M | \(|y_{0,0}-y_{0}^{0}|\) | \(|z_{0,0}-z_{0}^{0}|\) | \(t_{CPU}\) | \(t_{GPU}\) | speedup |
---|---|---|---|---|---|---|---|
1 | 128 | 364 | 9.36E−07 | 2.78E−05 | 0.14 | 0.91 | 0.15 |
1 | 256 | 512 | 3.89E−07 | 1.40E−05 | 0.37 | 1.73 | 0.21 |
1 | 512 | 726 | 1.74E−07 | 7.04E−06 | 1.06 | 3.57 | 0.30 |
1 | 1024 | 1024 | 8.22E−08 | 3.53E−06 | 2.91 | 6.96 | 0.42 |
2 | 128 | 1218 | 8.01E−08 | 8.61E−06 | 0.64 | 1.05 | 0.61 |
2 | 256 | 2048 | 2.03E−08 | 4.00E−06 | 2.06 | 1.88 | 1.10 |
2 | 512 | 3446 | 5.02E−09 | 1.92E−06 | 7.18 | 3.21 | 2.24 |
2 | 1024 | 5794 | 1.25E−09 | 9.41E−07 | 23.93 | 5.83 | 4.10 |
3 | 128 | 4096 | 1.44E−11 | 2.77E−08 | 2.71 | 1.04 | 2.61 |
3 | 256 | 8192 | 1.70E−12 | 3.50E−09 | 11.02 | 1.82 | 6.06 |
3 | 512 | 16,384 | 1.87E−13 | 4.41E−10 | 44.86 | 3.68 | 12.19 |
3 | 1024 | 32,768 | 2.05E−14 | 5.53E−11 | 180.30 | 10.08 | 17.89 |
4 | 128 | 4096 | 1.06E−11 | 1.69E−08 | 3.28 | 1.05 | 3.13 |
4 | 256 | 8192 | 1.20E−12 | 2.13E−09 | 13.57 | 1.84 | 7.36 |
4 | 512 | 16,384 | 2.57E−13 | 2.68E−10 | 55.16 | 3.84 | 14.35 |
4 | 1024 | 32,768 | 1.29E−14 | 3.34E−11 | 223.28 | 10.68 | 20.91 |
5 | 128 | 4096 | 1.46E−12 | 1.90E−08 | 3.86 | 1.06 | 3.63 |
5 | 256 | 8192 | 1.12E−12 | 2.40E−09 | 16.23 | 1.88 | 8.65 |
5 | 512 | 16,384 | 3.46E−14 | 3.02E−10 | 65.80 | 3.97 | 16.57 |
5 | 1024 | 32,768 | 9.77E−15 | 3.78E−11 | 267.79 | 11.33 | 23.64 |
6 | 128 | 4096 | 6.94E−12 | 1.84E−08 | 4.53 | 1.10 | 4.11 |
6 | 256 | 8192 | 7.71E−13 | 2.32E−09 | 18.97 | 1.93 | 9.84 |
6 | 512 | 16,384 | 1.07E−13 | 2.92E−10 | 77.64 | 4.23 | 18.35 |
6 | 1024 | 32,768 | 1.03E−14 | 3.65E−11 | 311.87 | 11.97 | 26.06 |