New Highly Efficient Families of Higher-Order Methods for Simple Roots, Permitting 𝑓^′(𝑥_𝑛)=0

Table 2

𝑓(𝑥)	𝑥0	LW8; (𝛼=0,𝛽=0)	TM8	SS8; (𝛼=1)	KW8; (𝛼=3)	SM8	MKM8; |𝜆11|=2	MOM8; |𝜆11|=2
Comparison of different optimal eight-order methods with the same total number of functional evaluations (TNFE = 12)
𝑓1(𝑥)	−1.51	C	C	C	C	C	4.05𝑒−258	1.52𝑒−262
	−1.51	C	C	C	C	C	4.05𝑒−258	1.52𝑒−262
Comparison of different optimal eight-order methods with respect to number of iterations
𝑓1(𝑥)	−1.51	C	C	C	C	C	4	4
	−1.51	C	C	C	C	C	4	4