Research Article
Two Optimal Eighth-Order Derivative-Free Classes of Iterative Methods
Table 2
Results of convergence for different derivative-free methods.
| | Guess | | (1.1) | (3.1) | (3.3) | (3.2) | (2.8) |
| | | IT |
9
|
4
|
3
|
3
|
3
| | TNE |
18
|
12
|
12
|
12
|
12
|
0.3
| | | | | | |
0.2
| | | | | | |
| | | IT |
9
|
4
|
3
|
3
|
3
| | TNE |
18
|
12
|
12
|
12
|
12
| −0.9 | | | | | | | −0.4 | | | | | | |
| | | IT |
9
|
4
|
3
|
3
|
3
| | TNE |
18
|
12
|
12
|
12
|
12
|
1.25
| | | | | | |
1.6
| | | | | | |
| | | IT |
9
|
4
|
3
|
3
|
3
| | TNE |
18
|
12
|
12
|
12
|
12
| −1.3 | | | | | | | −1 | | | | | | |
| | | IT |
10
|
5
|
3
|
3
|
3
| | TNE |
20
|
15
|
12
|
12
|
12
|
0
| | | | | | | −0.7 | | | | | | |
| | | IT |
8
|
4
|
3
|
3
|
3
| | TNE |
16
|
12
|
12
|
12
|
12
| −2.2 | | | | | | | −1.7 | | | | | | |
| | | IT |
9
|
4
|
3
|
3
|
3
| | TNE |
18
|
12
|
12
|
12
|
12
|
3
| | | | | | |
0.6
| | | | | | |
| | | IT |
9
|
4
|
3
|
3
|
3
| | TNE |
18
|
12
|
12
|
12
|
12
|
1.3
| | Div. | | | | |
0.3
| | | | | | |
| | | IT |
9
|
4
|
3
|
3
|
3
| | TNE |
18
|
12
|
12
|
12
|
12
|
0.6
| | | | | | |
0.4
| | | | Div. | | |
| | | IT |
8
|
4
|
3
|
3
|
3
| | TNE |
16
|
12
|
12
|
12
|
12
|
1.36
| | | | | | |
1.32
| | | | | | |
| | | IT |
9
|
4
|
3
|
3
|
3
| | TNE |
18
|
12
|
12
|
12
|
12
| −1 | | | | | Div. | |
0.3
| | | | | | |
| | | IT |
9
|
4
|
3
|
5
|
3
| | TNE |
18
|
12
|
12
|
20
|
12
| 1.4 | | | | | | |
1.3
| | Div. | | Div. | | |
| | | IT |
18
|
4
|
3
|
3
|
3
| | TNE |
36
|
12
|
12
|
12
|
12
| 0.3 | | | | | | |
0.8
| |
0.1
| | | | |
| | | IT |
8
|
4
|
3
|
3
|
3
| | TNE |
16
|
12
|
12
|
12
|
12
| 0.2 | | | | | | |
0.5
| | | | | | |
| | | IT |
8
|
4
|
3
|
3
|
3
| | TNE |
16
|
12
|
12
|
12
|
12
| 0.3 | | | | | | |
0.4
| | | | | | |
| | | IT |
9
|
4
|
3
|
3
|
3
| | TNE |
18
|
12
|
12
|
12
|
12
| 9 | | | | | | |
9.2
| | | | | | |
| | | IT |
9
|
4
|
3
|
3
|
3
| | TNE |
18
|
12
|
12
|
12
|
12
| 0.1 | | Div. | | | | |
0.8
| | | | | | |
| | | IT |
9
|
4
|
3
|
3
|
3
| | TNE |
18
|
12
|
12
|
12
|
12
| 0.3 | | | | | | |
0.2
| | | | | | |
| | | IT |
10
|
4
|
3
|
3
|
3
| | TNE |
20
|
12
|
12
|
12
|
12
| −0.7 | | | | | | | −0.9 | | Div. | | Div. | Div. | |
| | | IT |
8
|
4
|
3
|
3
|
3
| | TNE |
16
|
12
|
12
|
12
|
12
| 0.9 | | | | | | |
0.7
| | | | | | |
|
|