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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