Research Article
A Two-Point Newton Method Suitable for Nonconvergent Cases and with Super-Quadratic Convergence
Table 1
Comparison of results of iterations of the two-point Newton method with Newton and secant methods.
| Function | Root | Starting point | Secant method | Newton method | Two-point Newton method |
| | 1.365230013414100 | 0.5 | 10 | 8 | 6 | 1 | 9 | 6 | 5 | | −1.404491648215340 | −1 | 9 | 7 | 5 | −3 | 9 | 7 | 6 | | −2.0000000000000 | −3 | 168 | 119 | 83 | 1.4 | 116 | 81 | 60 | | 2.00000000000000 | 1.5 | 25 | 17 | 8 | 2.5 | 12 | 8 | 6 | 3.5 | 16 | 11 | 8 | = sin() · + ln() | −0.603231971557215 | −0.8 | 8 | 7 | 5 | −0.65 | 8 | 5 | 4 | | 3.000000000000000 | 4 | 29 | 20 | 14 | 4.5 | 39 | 28 | 18 | | 1.857183860207840 | 2 | 8 | 5 | 4 | 0.5 | 11 | 8 | 5 |
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