Basins of Attraction for Various Steffensen-Type Methods

Table 1

Results of chaotic comparisons for different derivative-free methods.

Method	Test 1	Test 2	Test 4	Test 5	Average
(10) with 𝛽=1	3	4	3	3	13/4
(10) with 𝛽=−0.001	2	3	2	2	9/4
(11) with 𝛽=1	3	4	3	3	13/4
(11) with 𝛽=−0.001	2	3	2	2	9/4
(13)	4	4	4	3	15/4
(15)	4	4	4	3	15/4
(17) with 𝛽=1	3	3	3	3	12/4
(17) with 𝛽=−0.001	2	2	1	2	7/4
(19) with 𝛽=1	2	2	3	3	10/4
(19) with 𝛽=−0.001	1	1	1	1	4/4