Ajout de la figure Spare and full polynomial with or no Log.exp

[kahina_paper1.git] / paper.tex

diff --git a/paper.tex b/paper.tex
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+++ b/paper.tex
@@ -662,7 +662,7 @@ The figure 2 show that, the best execution time for both sparse and full polynom
 In this experiment we report the performance of log.exp solution describe in ~\ref{sec2} to compute very high degrees polynomials.   
 \begin{figure}[H]
 \centering
 In this experiment we report the performance of log.exp solution describe in ~\ref{sec2} to compute very high degrees polynomials.   
 \begin{figure}[H]
 \centering

-  \includegraphics[width=0.8\textwidth]{figures/log_exp}
+  \includegraphics[width=0.8\textwidth]{figures/sparse_full_explog}

 \caption{The impact of exp-log solution to compute very high degrees of  polynomial.}
 \label{fig:01}
 \end{figure}
 \caption{The impact of exp-log solution to compute very high degrees of  polynomial.}
 \label{fig:01}
 \end{figure}


@@ -672,12 +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}
+%\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.