Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space

Table 2

Error computing results (|𝑥_𝑛−𝑥^∗|).

Step	Newton’s method	Halley’s method (3)	Method (16) with 𝑝=2/3, 𝛼=1	Method (16) with 𝑝=1/2, 𝛼=0
𝑛=1	2.56574×10^−2	2.13749×10^−3	1.58011×10^−3	5.74362×10^−3
𝑛=2	4.8337×10^−4	3.04697×10^−9	1.19327×10^−11	1.98875×10^−7
𝑛=3	1.75164×10^−7	8.84002×10^−27	3.90354×10^−44	8.35734×10^−21
𝑛=4	2.30119×10^−14	2.15878×10^−79	4.47038×10^−174	6.20201×10^−61