Theory and Modern Applications
Table 10 Exact and LNN neural network results
Input points \(x_{k}\) | Exact results | LNN results | Absolute error |
|---|---|---|---|
0 | 1 | 1 | 0 |
0.1 | 0.9966699984131 | 0.9966699984129 | 1.8e–13 |
0.2 | 0.9867198985254 | 0.9867198985252 | 2.2e–13 |
0.3 | 0.9702688457452 | 0.9702688457450 | 2.3e–13 |
0.4 | 0.9475135272247 | 0.9475135272245 | 2.3e–13 |
0.5 | 0.9187253698655 | 0.9187253698653 | 2.3e–13 |
0.6 | 0.8842466786034 | 0.8842466786032 | 2.2e–13 |
0.7 | 0.8444857748514 | 0.8444857748511 | 2.2e–13 |
0.8 | 0.7999112103978 | 0.7999112103976 | 2.1e–13 |
0.9 | 0.7510451462491 | 0.7510451462489 | 2.0e–13 |
1 | 0.6984559986366 | 0.6984559986364 | 1.8e–13 |