A Two-Parameter Family of Fourth-Order Iterative Methods with Optimal Convergence for Multiple Zeros

Table 2

Convergence behavior with 𝑓(𝑥)=cos(𝜋𝑥²/6)log(𝑥²−√3𝑥+1),  (𝑚,𝜆,𝜌)=(2,5,5),  𝛼=√3.

𝑛	𝑥𝑛	|𝑓(𝑥𝑛)|	|𝑥𝑛−𝛼|	|𝑒𝑛+1/𝑒^4𝑛|	𝜂
0	1.58	0.0716114	0.152051		0.02152876768
1	1.73207355929649	1.62622×10^−9	0.0000227517	0.04256566818
2	1.73205080756888	1.04639×10^−40	5.77127×10^−21	0.02153842658
3	1.73205080756888	1.79209×10^−165	2.38839×10^−83	0.02152876768
4	1.73205080756888	0.0×10^−599	0.0×10^−299