Table 14 System (29): Performance of the classical and generalized Newton methods with one million randomly generated starting points in domains of various sizes
\(s_{i}(x)\) | \([-3,3]^{2}\) | \([-10,10]^{2}\) | \([-100,100]^{2}\) | CPU time/successful iter [sec] | |||
|---|---|---|---|---|---|---|---|
Ave iter | Success rate [%] | Ave iter | Success rate [%] | Ave iter | Success rate [%] | ||
\(x_{i}\) | 10.5 | 58.8 | 11.9 | 41.2 | – | 0.0 | 6.3 × 10−6 |
\(x_{i}^{3}\) | 8.0 | 76.7 | 8.5 | 48.9 | 8.8 | 17.7 | 9.5 × 10−6 |
\(\sinh (x_{i})\) | 8.9 | 74.9 | 11.1 | 17.4 | – | 0.0 | 6.9 × 10−6 |
\(e^{x_{i}}\) | 10.8 | 62.4 | 12.3 | 2.2 | – | 0.0 | 1.0 × 10−5 |
\(\tan {x_{i}}\) | 9.2 | 3.2 | 9.8 | 0.6 | – | 0.0 | 7.3 × 10−6 |