Research Article
A Two-Point Newton Method Suitable for Nonconvergent Cases and with Super-Quadratic Convergence
Table 2
Results of application of the proposed method for cases in which Newton or secant method fails to converge.
| Function | Root | Comparison of number of iterations required | Starting point | Secant method | Newton method | Two-point Newton method |
| | 1.887207676120680 | 1 | 11 | Oscillates | 7 | 0.5 | 23 | Oscillates | 6 | | 1.000000000000000 | 3.0 | Fails | Fails | 5 | = arctan | 0.0000000000000 | 3.0 | Diverges | Diverges | 6 | −3.0 | Diverges | Diverges | 6 | | −1.167303978261420 | 2.0 | Oscillates | Oscillates | 12 | 3.0 | 14 | Oscillates | 15 | | 4.00000000000000 | 3.0 | 10 | Oscillates | 7 | 5.0 | 8 | Oscillates | 6 | | 0.00000000000000 | 1.0 | Oscillates | Diverges | 101 | −1.0 | Oscillates | Diverges | 101 | | 1.679630610428450 | 3.0 | Diverges | Diverges | 8 | 0.101025848315685 | −1.0 | Diverges | Diverges | 11 |
|
|