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

Table 2

Comparative of the iterative methods with the nonlinear system of equations of the GPS.

Method	𝑥^(0)	Iter	ACOC	||𝑥^(𝑘+1)−𝑥^(𝑘)||	||𝐹(𝑥^(𝑘+1))||	𝑥
𝑁	(0,0,0,0)^𝑇	12	2	0.6𝑒−374	0.830𝑒−739	𝑥^∗
𝑆		7	4	0.173𝑒−767	0.2𝑒−1991	𝑥^∗
𝑀4		7	4	0.823𝑒−512	0.1𝑒−1991	𝑥^∗
𝑀5		7	5	0.222𝑒−814	0.3𝑒−1991	𝑥^𝑠
𝑁	(10^6,10^6,10^6,10^6)^𝑇	15	2	0.421𝑒−317	0.537𝑒−627	𝑥^𝑠
𝑆		8	4	0.739𝑒−799	0.1𝑒−1991	𝑥^∗
𝑀4		7	4	0.191𝑒−735	0	𝑥^∗
𝑀5		8	5	0.104𝑒−563	0.1𝑒−1991	𝑥^𝑠
𝑁	(−10^4,−10^4,−10^4,−10^4)^𝑇	12	2	0.371𝑒−381	0.317𝑒−753	𝑥^∗
𝑆		7	4	0.138𝑒−784	0.3𝑒−1991	𝑥^∗
𝑀4		7	4	0.704𝑒−520	0	𝑥^∗
𝑀5		7	4.9968	0.510𝑒−692	0.1𝑒−1991	𝑥^𝑠