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

Table 4

Convergence behavior with 𝑓(𝑥)=(1−sin(𝑥²))(log(2𝑥²−𝜋+1))⁴,  (𝑚,𝜆,𝜌)=(6,1,−1),  𝛼=−𝜋/2.

𝑛	𝑥𝑛	|𝑓(𝑥𝑛)|	|𝑥𝑛−𝛼|	|𝑒𝑛+1/𝑒^4𝑛|	𝜂
0	−1.18	0.000601837	0.0733141		0.3470127318
1	−1.25334379618481	1.35039×10^−24	0.0000296589	1.026605711
2	−1.25331413731550	7.41245×10^−109	2.68363×10^−19	0.3468196331
3	−1.25331413731550	6.74576×10^−446	1.79984×10^−75	0.3470127318
4	−1.25331413731550	4.62631×10^−1794	3.64139×10^−300