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Table 5 Values of m , k , and \(\pmb{\varepsilon_{k}}\) for Example 7.4 ( \(\pmb{{\mathscr{R} = 0.018685}}\) )

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 15 0.007235 1.588799 × 10−3 17 1.057241 × 10−18 1.574672 × 10−52
2 11 0.000001 1.731641 × 10−7 12 2.763909 × 10−30 2.863869 × 10−144
3 9 0.000026 4.171842 × 10−6 10 5.167701 × 10−32 2.328540 × 10−213
4 8 0.000032 5.141616 × 10−6 9 7.830010 × 10−40 3.487627 × 10−344
5 7 0.010766 2.954474 × 10−3 8 1.468181 × 10−20 2.870206 × 10−208
6 7 0.000002 4.201055 × 10−7 8 7.096655 × 10−71 6.481892 × 10−900
7 7 0.000000 9.445503 × 10−15 8 3.169914 × 10−196 2.445585 × 10−2,918
8 6 0.010675 2.911647 × 10−3 7 8.218559 × 10−31 3.538870 × 10−495
9 6 0.000281 4.462548 × 10−5 7 2.324176 × 10−64 1.205364 × 10−1,190
10 6 0.000000 1.231259 × 10−7 7 1.392265 × 10−124 1.840079 × 10−2,580
30 5 0.000000 2.416285 × 10−34 5 2.416285 × 10−34 1.294365 × 10−1,987