Optimal High-Order Methods for Solving Nonlinear Equations

Table 3

Comparison of modified-Gauss schemes for Orbit II.

	|(𝑥1−𝑥0)|	|𝐹(𝑥1)|	|(𝑥2−𝑥1)|	|𝐹(𝑥2)|	|(𝑥3−𝑥2)|	|𝐹(𝑥3)|	ACOC
FP	0.2397𝑒−1	—	0.1132𝑒−2	—	0.5163𝑒−4	—	1.011
K8	0.2289𝑒−1	0.2830𝑒−15	0.2707𝑒−15	0.7343𝑒−113	0.7023𝑒−113	0.5810𝑒−796	7.007
S8	0.2289𝑒−1	0.6075𝑒−17	0.5809𝑒−17	0.8328𝑒−142	0.7964𝑒−142	0.1039𝑒−1140	8.006
M8	0.2289𝑒−1	0.3696𝑒−17	0.3534𝑒−17	0.9933𝑒−144	0.9500𝑒−144	0.2705𝑒−1156	8.005
T16	0.2289𝑒−1	0.2913𝑒−45	0.2786𝑒−45	0.4103𝑒−748	0.3924𝑒−748	0.0	16.000
S16	0.2289𝑒−1	0.1482𝑒−34	0.1417𝑒−34	0.4368𝑒−556	0.4195𝑒−556	0.0	16.010
M16	0.2289𝑒−1	0.4590𝑒−34	0.4389𝑒−34	0.1062𝑒−557	0.1016𝑒−557	0.0	16.000