Table 18 System (31): 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 [%] | ||
\(x_{i}\) | 7.8 | 80.1 | 10.5 | 81.1 | 12.2 | 4.2 | 3.7 × 10−6 |
\(x_{i}^{3}\) | 7.8 | 68.6 | 8.1 | 69.7 | 8.7 | 67.3 | 6.2 × 10−6 |
\(\sinh (x_{i})\) | 6.9 | 78.5 | 8.4 | 25.0 | 8.3 | 0.2 | 3.9 × 10−6 |
\(e^{x_{i}}\) | 8.6 | 81.4 | 10.9 | 27.6 | 10.9 | 0.3 | 5.1 × 10−6 |
\(\tan {x_{i}}\) | 6.7 | 34.9 | 7.3 | 24.4 | 7.9 | 0.4 | 3.9 × 10−6 |