Table 6 System (25): Performance of the classical and generalized Newton methods with one million randomly generated starting points in domains of various sizes
\(s_{i}(x)\) | \([-3,3]^{2}\) | \([-10,10]^{2}\) | CPU time/successful iter [sec] | ||
|---|---|---|---|---|---|
Ave iter | Success rate [%] | Ave iter | Success rate [%] | ||
\(x_{i}\) | 6.6 | 25.0 | 6.7 | 2.4 | 2.7 × 10−6 |
\(x_{i}^{3}\) | 7.3 | 12.3 | 7.3 | 1.1 | 4.6 × 10−6 |
\(\sinh (x_{i})\) | 6.2 | 17.4 | 6.2 | 1.6 | 2.9 × 10−6 |
\(e^{x_{i}}\) | 7.8 | 98.3 | 9.6 | 53.3 | 6.7 × 10−6 |
\(\tan {x_{i}}\) | 6.1 | 9.4 | 6.4 | 10.0 | 2.9 × 10−6 |