Table 10 System (27): 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 [%] | ||
\(x_{i}\) | 7.0 | 98.6 | 9.7 | 99.3 | 12.2 | 9.8 | 3.7 × 10−6 |
\(x_{i}^{3}\) | 6.1 | 98.6 | 6.3 | 99.7 | 6.8 | 100.0 | 6.1 × 10−6 |
\(\sinh (x_{i})\) | 5.9 | 99.8 | 7.9 | 34.8 | 7.8 | 0.3 | 4.1 × 10−6 |
\(e^{x_{i}}\) | 7.1 | 98.7 | 10.4 | 42.4 | 10.4 | 0.4 | 4.7 × 10−6 |
\(\tan {x_{i}}\) | 6.7 | 70.7 | 7.3 | 57.5 | 7.8 | 3.3 | 4.0 × 10−6 |