## 5 Numerical Examples
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **Initial Guess** & \(m\) & \(\boldsymbol{\Omega(E_{f}(x^{(m)}))}\) & \(k\) & \(\boldsymbol{\varepsilon_{f}(x^{(k)})}\) & \(\boldsymbol{\tau_{n}}\) & \(\boldsymbol{\varepsilon_{k}}\) \\ \hline \multirow{4}{*}{\(MWM\)} & \(x^{(0)}\) & \multicolumn{6}{c}{The method diverges} \\  & \(y^{(0)}\) & \(18\) & \(1.901188\) & \(21\) & \(1.877\times 10^{-5}\) & \(0.171573\) & \(1.051\times 10^{-7}\) \\  & \(z^{(0)}\) & \(20\) & \(1.431314\) & \(23\) & \(1.904\times 10^{-7}\) & \(0.171573\) & \(1.067\times 10^{-9}\) \\  & \(t^{(0)}\) & \(17\) & \(1.787441\) & \(20\) & \(7.297\times 10^{-6}\) & \(0.171573\) & \(4.087\times 10^{-8}\) \\ \hline \multirow{4}{*}{\(WM\)} & \(x^{(0)}\) & \(N/A\) & \(N/A\) & \(68\) & \(4.589\times 10^{-5}\) & \(0.171573\) & \(2.571\times 10^{-7}\) \\  & \(y^{(0)}\) & \(-\) & \(-\) & \(33\) & \(4.304\times 10^{-6}\) & \(0.171573\) & \(2.411\times 10^{-8}\) \\  & \(z^{(0)}\) & \(-\) & \(-\) & \(34\) & \(6.942\times 10^{-5}\) & \(0.171573\) & \(3.889\times 10^{-7}\) \\  & \(t^{(0)}\) & \(-\) & \(-\) & \(34\) & \(3.435\times 10^{-8}\) & \(0.171573\) & \(1.924\times 10^{-10}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical data for Example 1. **Example 3** ([26], Example 2, [29], Example 2). : _In this example, we consider the following polynomial:_  
\[f(z)=z^{20}-1 \tag{51}\]  
_for which [PERSON] and [PERSON] [26] have failed to find a suitable initial vector to use WM. The basins of attraction of the roots of (51) and the convergence areas are obtained by MWM and WM in the square_  
\[\{x\in\mathbb{C}\colon\left|Re(x)\right|\leq 3\text{ and }\left|Im(x)\right|\leq 3\}\]  
_replacing the fifth coordinate (randomly chosen) of [PERSON]'s initial approximation (46). For the numerical test, we take [PERSON]'s initial guess \(x^{(0)}\) and the initial vectors \(y^{(0)}\) and \(z^{(0)}\) which are obtained from \(x^{(0)}\) replacing its fifth coordinate by the randomly generated numbers \(0.89\ldots+1.86\ldots i\) and \(0.43\ldots-0.16\ldots i\) from the colored area and the bad basins of MWM (Figure 4), respectively._ \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **Initial Guess** & \(m\) & \(\boldsymbol{\Omega(E_{f}(x^{(m)}))}\) & \(\boldsymbol{k}\) & \(\boldsymbol{\mathcal{E}_{f}(x^{(k)})}\) & \(\boldsymbol{\tau_{n}}\) & \(\boldsymbol{\varepsilon_{k}}\) \\ \hline \multirow{4}{*}{\(MWM\)} & \(x^{(0)}\) & 37 & 1.286425 & 40 & \(4.938\times 10^{-11}\) & 0.075236 & \(3.764\times 10^{-11}\) \\  & \(y^{(0)}\) & 35 & 1.303345 & 37 & \(9.212\times 10^{-8}\) & 0.075236 & \(7.148\times 10^{-8}\) \\  & \(z^{(0)}\) & & & The method diverges & & & \\ \hline \multirow{2}{*}{\(WM\)} & \(x^{(0)}\) & \(N/A\) & \(N/A\) & 31 & \(4.716\times 10^{-7}\) & 0.075236 & \(3.595\times 10^{-7}\) \\  & \(y^{(0)}\) & \(-\) & \(-\) & 29 & \(1.159\times 10^{-9}\) & 0.075236 & \(8.838\times 10^{-10}\) \\  & \(z^{(0)}\) & \(-\) & \(-\) & 29 & \(3.487\times 10^{-7}\) & 0.075236 & \(2.658\times 10^{-7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Numerical data for Example 2. Figure 3: Dynamical planes for Example 2. As can be seen from Table 4 the two methods converge in all considered cases but behave slightly worse when start from \(z^{(0)}\).