in fact, when the modulus of the roots are up than \textit{R} given in ~\ref{R},this exceed the limited number in the mantissa of floating points representations and can not compute the iterative function given in ~\ref{eq:Aberth-H-GS} to obtain the root solution, who justify the divergence of the classical Ehrlich-Aberth algorithm. However, applying log.exp solution given in ~\ref{sec2} took into account the limit of floating using the iterative function in(Eq.~\ref{Log_H1},Eq.~\ref{Log_H2}and allows to solve a very large polynomials degrees .
+\begin{figure}[H]
+\centering
+ \includegraphics[width=0.8\textwidth]{figures/log_exp_Sparse}
+\caption{The impact of exp-log solution to compute very high degrees of polynomial.}
+\label{fig:01}
+\end{figure}
%we report the performances of the exp.log for the Ehrlich-Aberth algorithm for solving very high degree of polynomial.
