Table 9 System (27): 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 | \(x_{i}\) | [0.08,1.5] | 1.2 | |
\(x_{i}^{3}\) | [0.08,0.44] | 0.3 | 4.0 | |
\(\sinh (x_{i})\) | [0.08,0.96] | 0.8 | 1.5 | |
2 | \(x_{i}\) | [0.09,1.6] | 1.0 | |
\(x_{i}^{3}\) | [0.09,0.5] | 0.3 | 3.3 | |
\(\sinh (x_{i})\) | [0.09,1.1] | 0.6 | 1.7 | |
3 | \(x_{i}\) | [0,2.9] | 2.7 | |
\(x_{i}^{3}\) | [0,1.5] | 1.4 | 1.9 | |
\(\sinh (x_{i})\) | [0,2.5] | 2.4 | 1.1 | |
4 | \(x_{i}\) | [0,2.3] | 1.2 | |
\(x_{i}^{3}\) | [0,0.94] | 0.4 | 3.0 | |
\(\sinh (x_{i})\) | [0,1.8] | 0.7 | 1.7 | |
5 | \(x_{i}\) | [0,0.14] | 0.05 | |
\(x_{i}^{3}\) | [0,37] | 29.8 | 0.002 | |
\(\sinh (x_{i})\) | [0,0.17] | 0.16 | 0.3 |