Table 3 System (24): 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 [%] | ||
\(x_{i}\) | 8.0 | 56.4 | 10.5 | 56.9 | 11.8 | 2.0 | 2.7 × 10−6 |
\(x_{i}^{3}\) | 7.1 | 77.0 | 8.9 | 78.6 | 12.3 | 36.2 | 4.7 × 10−6 |
\(\sinh (x_{i})\) | 7.9 | 67.7 | 9.0 | 25.7 | 9.0 | 0.3 | 2.9 × 10−6 |
\(e^{x_{i}}\) | 9.0 | 76.0 | 10.7 | 27.6 | 10.6 | 0.3 | 5.1 × 10−6 |
\(\tan {x_{i}}\) | 5.9 | 10.9 | 6.5 | 14.8 | 7.1 | 0.3 | 3.0 × 10−6 |