A New Class of Halley’s Method with Third-Order Convergence for Solving Nonlinear Equations

Table 3

Comparison with other third order methods.

Test		: number of iterations/: approximate asymptotic constants
		NM	CB	CH	SH	H0
1.68		6	7	7	7	4	4	3	3	3	3
			2.33	2.06	2.06	0.20	0.05	0.06	0.06	0.06	0.06
4.5		7	5	5	5	4	4	3	3	3	3
			0.23	0.23	0.22	0.18	3e-2	7e-3	6e-3	6e-3	6e-3
-1.3		5	5	4	4	4	3	3	3	3	3
			2.74	0.44	0.27	0.30	0.11	0.11	0.11	0.11	0.11
		6	6	5	4	4	3	3	3	3	3
1.4			7.41	3.33	2.77	0.88	0.10	0.09	0.09	0.09	0.09
1.4		5	5	4	4	4	3	3	3	3	3
			3.91	1.28	0.91	0.95	0.54	0.53	0.53	0.53	0.53
7		5	4	4	4	4	3	3	2	2	2
			3-2	3-2	3-2	2-2	3-4	8-7	_	_	_
-0.485		6	4	4	4	4	4	4	4	3	3
			1.74	1.68	1.61	0.81	0.39	0.47	0.47	0.47	0.47
1.1		5	5	4	4	4	3	3	3	3	3
			1.26	0.49	0.32	0.29	0.17	0.16	0.17	0.17	0.17
2.7		6	5	5	5	4	4	3	3	3	3
			4.11	6.82	5.57	1.34	0.86	1.01	1.03	1.48	1.02