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Table 4 Values of m , k , and \(\pmb{\varepsilon_{k}}\) for Example 7.3 ( \(\pmb{{\mathscr{R} = 0.033867}}\) )

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 18 0.000060 6.095859 × 10−5 20 1.620028 × 10−38 4.276235 × 10−114
2 12 0.015335 2.153155 × 10−2 14 1.095084 × 10−46 1.779476 × 10−230
3 10 0.018005 2.769333 × 10−2 12 8.917532 × 10−86 4.482714 × 10−596
4 9 0.005514 6.130790 × 10−3 10 4.221856 × 10−21 7.250879 × 10−184
5 9 0.000000 1.159694 × 10−15 10 5.021359 × 10−165 5.118016 × 10−1,808
6 8 0.000237 2.386016 × 10−4 9 8.455240 × 10−48 1.280870 × 10−612
7 8 0.000000 2.723047 × 10−17 8 2.723047 × 10−17 8.926059 × 10−249
8 7 0.018995 2.934241 × 10−2 8 2.885374 × 10−30 4.152134 × 10−503
9 7 0.002180 2.274734 × 10−3 8 3.792876 × 10−51 1.140751 × 10−958
10 7 0.000000 5.185525 × 10−7 8 1.620086 × 10−132 2.936276 × 10−2,768
30 5 0.000181 1.821419 × 10−4 6 1.395923 × 10−226 1.902920 × 10−13,777