Table 3 Superlinear functions with multiple roots
Number of iterations | Noor iteration | Picard iteration | Mann iteration | Ishikawa iteration | Agarwal et al. iteration | S-iteration | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
n |
|
|
|
|
|
|
|
|
|
|
|
|
0 | 0.944 | 0.999988 | 0.944 | 0.944 | 0.944 | 0.944 | 0.944 | 0.996513 | 0.944 | 0.996513 | 0.944 | 0.996513 |
1 | 1 | 0.999996 | 0.996513 | 0.996513 | 0.996513 | 0.981132 | 0.999988 | 0.998978 | 0.999988 | 0.999996 | 0.999988 | 0.999999 |
2 | 1 | 0.999998 | 0.999988 | 0.999988 | 0.999631 | 0.991812 | 0.999999 | 0.999568 | 1 | 1 | 1 | 1 |
3 | 1 | 0.999999 | 1 | 1 | 0.999932 | 0.995872 | 1 | 0.999784 | 1 | 1 | 1 | 1 |
4 | 1 | 1 | 1 | 1 | 0.999983 | 0.99771 | 1 | 0.999881 | 1 | 1 | 1 | 1 |
5 | 1 | 1 | 1 | 1 | 0.999995 | 0.998643 | 1 | 0.999929 | 1 | 1 | 1 | 1 |
6 | 1 | 1 | 1 | 1 | 0.999998 | 0.999155 | 1 | 0.999956 | 1 | 1 | 1 | 1 |
7 | 1 | 1 | 1 | 1 | 0.999999 | 0.999454 | 1 | 0.999972 | 1 | 1 | 1 | 1 |
8 | 1 | 1 | 1 | 1 | 1 | 0.999636 | 1 | 0.999981 | 1 | 1 | 1 | 1 |
9 | 1 | 1 | 1 | 1 | 1 | 0.999751 | 1 | 0.999987 | 1 | 1 | 1 | 1 |
– | – | – | – | – | – | – | – | – | – | – | – | – |
19 | 1 | 1 | 1 | 1 | 1 | 0.999987 | 1 | 0.999999 | 1 | 1 | 1 | 1 |
20 | 1 | 1 | 1 | 1 | 1 | 0.99999 | 1 | 0.999999 | 1 | 1 | 1 | 1 |
21 | 1 | 1 | 1 | 1 | 1 | 0.999992 | 1 | 1 | 1 | 1 | 1 | 1 |
22 | 1 | 1 | 1 | 1 | 1 | 0.999994 | 1 | 1 | 1 | 1 | 1 | 1 |
23 | 1 | 1 | 1 | 1 | 1 | 0.999995 | 1 | 1 | 1 | 1 | 1 | 1 |
– | – | – | – | – | – | – | – | – | – | – | – | – |
32 | 1 | 1 | 1 | 1 | 1 | 0.999999 | 1 | 1 | 1 | 1 | 1 | 1 |
33 | 1 | 1 | 1 | 1 | 1 | 0.999999 | 1 | 1 | 1 | 1 | 1 | 1 |
34 | 1 | 1 | 1 | 1 | 1 | 0.999999 | 1 | 1 | 1 | 1 | 1 | 1 |
35 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
36 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |