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Table 1 Numerical results for test functions

From: Three-point iterative algorithm in the absence of the derivative for solving nonlinear equations and their basins of attraction

Function

\({\varvec{x_{0}}}\)

\(|g_i(x_m)|,i=1,2,3,4,5, m=3,\) for 8th BM

\(\theta =1\)

\(\theta =-1\)

\(\theta =0.5\)

\(\theta =-0.5\)

COC

\(g_{1}(x_3)\)

\(-\)1.5

\(5.75\times 10^{-41}\)

\(5.75\times 10^{-41}\)

\(4.36\times 10^{-65}\)

\(4.36\times 10^{-65}\)

8.11

\(g_{2}(x_3)\)

\(-\)0.2

\(1.00\times 10^{-100}\)

\(1.00\times 10^{-100}\)

\(1.45\times 10^{-488}\)

\(1.45\times 10^{-488}\)

7.99

\(g_{3}(x_3)\)

1.5

\(3.00\times 10^{-500}\)

\(3.00\times 10^{-500}\)

\(3.00\times 10^{-500}\)

\(3.00\times 10^{-500}\)

8.00

\(g_{4}(x_3)\)

\(-\)1.7

\(3.00\times 10^{-499}\)

\(3.00\times 10^{-499}\)

\(3.00\times 10^{-499}\)

\(3.00\times 10^{-499}\)

8.00

\(g_{5}(x_3)\)

0.7

\(1.32\times 10^{-395}\)

\(1.32\times 10^{-395}\)

\(31.75\times 10^{-433}\)

\(31.75\times 10^{-433}\)

8.00