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Table 2 Comparison of different methods for solving test functions

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

Function \({\varvec{x_{0}}}\) The number of iteration
Previous methods Presented algorithm  
DM2 KM PFDM \(\theta =-1.0\) \(\theta =-0.5\) \(\theta =0.5\) \(\theta =1.0\) \(\alpha\)
\(g_1(x)\) \(-\)1.5 5 36 4 3 3 3 3 0.7390851332151606
\(-\)1.0 5 4 4 3 4 4 3  
\(-\)0.5 5 3 3 2 2 2 2  
0.0 4 3 3 2 2 2 2  
\(g_2(x)\) \(-\)0.2 3 3 3 2 2 2 2 0.5235987755982989
0.0 3 3 3 2 2 2 2  
0.5 2 2 2 1 1 1 2  
1.0 4 3 3 2 2 2 2  
\(g_3(x)\) 0.3 7 9 5 3 3 3 3 1.4044916482153412
0.5 9 6 5 3 3 3 3  
1.3 3 2 3 2 3 2 2  
1.5 3 2 3 2 2 2 2  
\(g_4(x)\) \(-\)1.7 3 2 3 2 3 3 2 \(-\)1.6716998816571610
\(-\)0.9 4 17 90 3 2 2 2  
\(-\)0.5 Div 23 5 Div 2 2 2  
0.0 Div 55 8 Div Div Div 2  
\(g_5(x)\) 0.5 6 3 4 3 2 2 2 0.8570567764718169
0.7 4 3 3 2 2 2 2  
1.1 Div 3 7 6 3 3 2  
2.5 4 3 9 2 2 2 3