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Table 3 Values of m , k , and \(\pmb{\varepsilon_{k}}\) for Example 7.2 ( \(\pmb{{\mathscr{R} = 0.043061}}\) )

From: On the convergence of high-order Ehrlich-type iterative methods for approximating all zeros of a polynomial simultaneously

N

m

\(\boldsymbol{E_{f}(x^{(m)})}\)

\(\boldsymbol{\varepsilon_{m}}\)

k

\(\boldsymbol{\varepsilon_{k}}\)

\(\boldsymbol{\varepsilon_{k + 1}}\)

1

6

0.036897

3.187918 × 10−2

9

3.967908 × 10−36

5.304009 × 10−106

2

5

0.000003

1.182714 × 10−6

6

6.112531 × 10−28

2.230412 × 10−134

3

4

0.000064

2.475020 × 10−5

5

2.446120 × 10−29

2.722168 × 10−197

4

4

0.000000

1.550670 × 10−11

5

3.838741 × 10−93

1.589981 × 10−827

5

3

0.005793

2.415745 × 10−3

4

9.532339 × 10−24

8.487351 × 10−248

6

3

0.000293

1.127450 × 10−4

4

9.565008 × 10−45

1.725858 × 10−565

7

3

0.000005

2.173198 × 10−6

4

4.018844 × 10−77

6.737932 × 10−1,138

8

3

0.000000

1.562375 × 10−8

4

1.162424 × 10−123

1.291370 × 10−2,080

9

3

0.000000

4.092421 × 10−11

4

4.245137 × 10−187

1.373908 × 10−3,530

10

3

0.000000

3.904607 × 10−14

4

4.643262 × 10−270

2.543247 × 10−5,644

30

2

0.000055

2.129417 × 10−5

3

5.721566 × 10−249

2.377023 × 10−15,106