Nonlinear Equations - UFRJ

104 [CH. 7: NEWTON ITERATION
13−3
1/32 1/16 1/10 1/8 √ 17
4
1 4.854 3.683 2.744 2.189 1.357
2 14.472 10.865 7.945 6.227 3.767
3 33.700 25.195 18.220 14.41 7.874
4 72.157 53.854 38.767 29.648 15.881
5 149.71 111.173 79.861 60.864 31.881
6 302.899 225.811 162.49 123.295 63.881
Table 7.2: Values of −log 2 (‖x i − ζ‖/β) in function of α and i.
2 63 2 − 3 √ 2
i = 5
i = 6
i = 4
2 31
i = 3
2 15
2 7
2 3
2
i = 1
i = 2
13−3 √ 17
4
Figure 7.5: Values of −log 2 (‖x i − ζ‖/β) in function of α for i = 1 to
6.