MAJ de quelque figures

[kahina_paper1.git] / paper.tex

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@@ -672,6 +672,12 @@ The figure 3, show a comparison between the execution time of the Ehrlich-Aberth
 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 . 
 
 
 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. 
 
 
 %we report the performances of the exp.log for the Ehrlich-Aberth algorithm for solving very high degree of polynomial.