New Families of Third-Order Iterative Methods for Finding Multiple Roots

Table 2

Comparison of various iterative methods for the function 𝑓₂(𝑥) under the same total number of function evaluations (TNFE) required by all methods.

Method	|𝑥𝑛−𝑥^⋆|	|𝑓(𝑥𝑛)|	COC
MNM	2.83𝑒−95	1.06𝑒−283	2.0000000
DM	1.88𝑒−109	3.11𝑒−326	3.0000000
VM	3.19𝑒−107	1.52𝑒−319	3.0000000
RM1	2.04𝑒−106	4.00𝑒−317	3.0000000
RM2	2.59𝑒−104	8.11𝑒−311	3.0000000
RM3	8.19𝑒−110	2.57𝑒−327	3.0000000
RM4	2.09𝑒−113	4.27𝑒−338	3.0000000
RM5	4.66𝑒−100	4.73𝑒−298	3.0000000
RM6	1.05𝑒−144	5.39𝑒−432	3.0000000

TNFE = 12.