Theory and Modern Applications
m | Newton’s method | Halley’s method | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
\(s_{0}=0.2\) | \(s_{0}=0.4\) | \(s_{0}=0.6\) | \(s_{0}=0.8\) | \(s_{0}=1.0\) | \(s_{0}=0.2\) | \(s_{0}=0.4\) | \(s_{0}=0.6\) | \(s_{0}=0.8\) | \(s_{0}=1.0\) | |
1 | 0.604011 | 1.305541 | 2.105771 | 3.00776 | 4.017051 | 0.603191 | 1.304704 | 2.104838 | 3.006644 | 4.01565 |
2 | 0.042234 | 1.48E−01 | 0.303846 | 5.05E−01 | 0.753495 | 0.054329 | 1.90E−01 | 0.392297 | 6.59E−01 | 0.995211 |
3 | 0.000274 | 3.25E−03 | 0.01249 | 3.10E−02 | 0.061341 | 0.000604 | 6.84E−03 | 0.025715 | 6.31E−02 | 0.124161 |
4 | 7.31E−08 | 7.33E−07 | 2.17E−05 | 1.46E−04 | 0.000578 | 9.11E−08 | 8.24E−06 | 1.34E−04 | 0.000813 | 0.003036 |
5 | 2.28E−11 | 2.29E−10 | 6.71E−09 | 4.22E−08 | 1.25E−07 | 2.58E−11 | 2.32E−09 | 3.41E−08 | 8.56E−08 | 1.15E−06 |
6 | 7.11E−15 | 7.19E−14 | 2.10E−12 | 1.32E−11 | 3.91E−11 | 6.22E−15 | 6.55E−13 | 9.64E−12 | 2.42E−11 | 3.26E−10 |
7 | 0 | 0 | 8.88E−16 | 4.44E−15 | 1.07E−14 | 8.88E−16 | 0 | 2.66E−15 | 6.22E−15 | 9.15E−14 |
8 | 0 | 0 | 0 | 0 | 1.78E−15 | 8.88E−16 | 0 | 8.88E−16 | 0 | 8.88E−16 |
9 | 0 | 0 | 0 | 0 | 0 | 8.88E−16 | 0 | 8.88E−16 | 0 | 8.88E−16 |
10 | 0 | 0 | 0 | 0 | 0 | 8.88E−16 | 0 | 8.88E−16 | 0 | 8.88E−16 |