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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