Table 13 System (29): Asymptotic error constants of the classical and generalized Newton methods
Soln | \(s_{i}(x)\) | \([\|\mu (x^{*})\|/2, \|\rho (x^{*})\|/2]\) | λ | \(\lambda _{N}/\lambda _{\mathrm{GN}}\) |
|---|---|---|---|---|
1 | \(x_{i}\) | [0,3.4] | 0.7 | |
\(x_{i}^{3}\) | [0,1.2] | 0.2 | 3.5 | |
\(\sinh x_{i}\) | [0,2.7] | 1.3 | 0.5 | |
2 | \(x_{i}\) | [0,3.1] | 0.8 | |
\(x_{i}^{3}\) | [0,1.0] | 0.4 | 2 | |
\(\sinh x_{i}\) | [0,2.4] | 0.5 | 1.6 | |
3 | \(x_{i}\) | [0,3.1] | 0.9 | |
\(x_{i}^{3}\) | [0,0.9] | 0.4 | 2.3 | |
\(\sinh x_{i}\) | [0,2.3] | 0.8 | 1.1 |