Research Article
Some New Variants of Cauchy's Methods for Solving Nonlinear Equations
Table 2
Comparison of the methods and Newton's method.
| | | | | | | | | | NEF | | | | NM | NSM | OM | LM6 | LM1 | NM | NSM | OM | LM6 | LM1 |
| | −0.5 | 131 | 10 | 14 | 27 | 9 | 262 | 30 | 42 | 81 | 27 | | 2 | 5 | 4 | 3 | 3 | 3 | 10 | 12 | 9 | 9 | 9 |
| | 0 | 4 | 3 | 2 | 2 | 2 | 8 | 9 | 6 | 6 | 6 | | 0.5 | 4 | 3 | 2 | 2 | 2 | 8 | 9 | 6 | 6 | 6 |
| | −3 | 6 | 4 | 3 | 3 | 3 | 12 | 12 | 9 | 9 | 9 | | −5 | 7 | 5 | 4 | 4 | 4 | 14 | 15 | 12 | 12 | 12 |
| | 1 | 7 | 4 | 4 | 4 | 4 | 14 | 12 | 12 | 12 | 12 | | 2 | 6 | 4 | 4 | 4 | 4 | 12 | 12 | 12 | 12 | 12 |
| | 2.5 | 6 | 4 | 3 | 3 | 4 | 12 | 12 | 9 | 9 | 12 | | 3.5 | 7 | 5 | 4 | 4 | 4 | 14 | 15 | 12 | 12 | 12 |
| | −0.3 | 5 | 4 | 3 | 4 | 3 | 10 | 12 | 9 | 12 | 9 | | 2.7 | 6 | 4 | 3 | 3 | 3 | 12 | 12 | 9 | 9 | 9 |
| | 1 | 6 | 4 | 3 | 4 | 3 | 12 | 12 | 9 | 12 | 9 | | 3 | 6 | 4 | 3 | 3 | 3 | 12 | 12 | 9 | 9 | 9 |
| | 3.25 | 8 | 5 | 5 | 4 | 5 | 16 | 15 | 15 | 12 | 15 | | 3.45 | 11 | 7 | 6 | 6 | 6 | 22 | 21 | 18 | 18 | 18 |
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