Theory and Modern Applications
Table 2 Comparison of optimal 3rd order methods
Method | \(\vert \text{x}_{i}^{ ( 6 ) } - \alpha \vert \) | \(\vert \text{f}_{i}^{(6)}\text{(x}_{i}) \vert \) | CPU | ρ |
|---|---|---|---|---|
Single root finding iterative methods | ||||
\(f_{4}(x)=\frac{x^{3}+2.87x^{2}-10.28}{4.62}-x\), \(x_{0}=2.5\), CO = 8, \(\alpha = \frac{16}{7}\) | ||||
Q1 | 2.7e−32 | 3.9e−42 | 0.032 | 2.99 |
E1 | 1.2e−25 | 1.8e−34 | 0.047 | 2.97 |
E2 | 3.5e−26 | 5.1e−35 | 0.047 | 3.00 |
E3 | 2.7e−33 | 1.4e−42 | 0.034 | 3.00 |
E4 | 5.2e−17 | 7.6e−26 | 0.046 | 2.99 |
E5 | 1.1e−33 | 3.4e−42 | 0.032 | 3.00 |
E6 | 1.0e−24 | 1.4e−33 | 0.045 | 2.98 |