Fourth- and Fifth-Order Methods for Solving Nonlinear Systems of Equations: An Application to the Global Positioning System

Table 1

Comparative of the iterative methods with nonlinear systems (a) to (c).

Function	𝑥^(0)	Method	Iter	ACOC	||𝑥^(𝑘+1)−𝑥^(𝑘)||	||𝐹(𝑥^(𝑘+1))||
(a)	(2,2)^𝑇	𝑁	13	2	0.163𝑒−338	0
		𝑆	7	4	0.962𝑒−270	0
		𝑀4	7	4	0.140𝑒−805	0
		𝑀5	7	5	0.893𝑒−831	0
(b)	(−0.1,−0.1)^𝑇	𝑁	9	2	0.94𝑒−307	0.28𝑒−921
		𝑆	5	4	0.53𝑒−276	0.83𝑒−1106
		𝑀4	5	4	0.98𝑒−300	0.32𝑒−1801
		𝑀5	5	5	0.435𝑒−647	0.1𝑒−3941
(c); 𝑛=99	(2,2,…,2)^𝑇	𝑁	11	2	0.535𝑒−488	0.286𝑒−976
		𝑆	6	4	0.113𝑒−408	0.960𝑒−1636
		𝑀4	6	4	0.380𝑒−704	0
		𝑀5	6	5	0.122𝑒−1201	0