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 | 0.487617 | 0.891569 | 1.202993 | 1.407814 | 1.485109 | 0.487722 | 0.891834 | 1.203474 | 1.408578 | 1.486244 |
2 | 0.101684 | 3.44E−01 | 0.653431 | 9.74E−01 | 1.258505 | 0.106265 | 3.56E−01 | 0.668984 | 9.90E−01 | 1.270771 |
3 | 0.004491 | 5.07E−02 | 0.182979 | 4.14E−01 | 0.72559 | 0.005185 | 5.68E−02 | 0.199315 | 4.40E−01 | 0.757881 |
4 | 1.26E−05 | 1.14E−03 | 0.014409 | 0.073158 | 0.226095 | 1.69E−05 | 1.51E−03 | 1.80E−02 | 8.68E−02 | 0.255888 |
5 | 1.13E−08 | 1.57E−06 | 0.000101 | 0.002343 | 0.021949 | 1.54E−08 | 2.39E−06 | 1.63E−04 | 3.48E−03 | 2.96E−02 |
6 | 1.01E−11 | 1.41E−09 | 9.49E−08 | 4.43E−06 | 0.000225 | 1.39E−11 | 2.16E−09 | 1.59E−07 | 8.62E−06 | 4.22E−04 |
7 | 9.06E−15 | 1.26E−12 | 8.48E−11 | 3.97E−09 | 2.22E−07 | 1.25E−14 | 1.95E−12 | 1.44E−10 | 7.82E−09 | 4.62E−07 |
8 | 6.94E−18 | 1.12E−15 | 7.58E−14 | 3.55E−12 | 1.99E−10 | 6.94E−18 | 1.76E−15 | 1.30E−13 | 7.06E−12 | 4.17E−10 |
9 | 0 | 1.39E−17 | 6.94E−17 | 3.16E−15 | 1.78E−13 | 6.94E−18 | 6.94E−18 | 1.25E−16 | 6.37E−15 | 3.77E−13 |
10 | 0 | 6.94E−18 | 6.94E−18 | 6.94E−18 | 1.67E−16 | 6.94E−18 | 0 | 6.94E−18 | 6.94E−18 | 3.33E−16 |