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Table 1 Values of m , k , and \(\pmb{\varepsilon_{k}}\) for Example 7.1 ( \(\pmb{{\mathscr{R} = 0.125}}\) )

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

2

0.010032

1.457548 × 10−2

4

4.385760 × 10−21

8.919073 × 10−63

2

1

0.067725

1.242914 × 10−1

3

1.347060 × 10−38

7.284576 × 10−193

3

1

0.015716

2.300541 × 10−2

3

1.825502 × 10−106

5.054741 × 10−744

4

1

0.002730

3.887455 × 10−3

2

1.330837 × 10−25

3.543773 × 10−230

5

1

0.001215

1.722883 × 10−3

2

4.720064 × 10−37

2.999643 × 10−407

6

1

0.000206

2.927439 × 10−4

2

1.060096 × 10−50

5.523501 × 10−657

7

1

0.000081

1.155284 × 10−4

2

6.261239 × 10−67

3.252761 × 10−1,002

8

1

0.000014

1.986052 × 10−5

2

6.080606 × 10−85

3.570038 × 10−1,439

9

1

0.000005

7.910775 × 10−6

2

1.309022 × 10−105

1.170454 × 10−2,002

10

1

0.000000

1.366899 × 10−6

2

4.301615 × 10−128

8.477451 × 10−2,683

100

1

0.000000

1.820743 × 10−57

1

1.820743 × 10−57

3.460397 × 10−11,451