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Journal of the Egyptian Mathematical Society

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

 
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