X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/blobdiff_plain/01adae2d410b21d0a75e877e50750a70b435422d..81d003bcad3c84329faf00f78370647031ff76f5:/paper.tex

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@@ -655,12 +655,22 @@ The figure 2 show that, the best execution time for both sparse and full polynom
 
 \subsubsection{The impact of exp-log solution to compute very high degrees of  polynomial}
 
+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}
 \caption{The impact of exp-log solution to compute very high degrees of  polynomial.}
 \label{fig:01}
 \end{figure}
+
+The figure 3, show a comparison between the execution time of the Ehrlisch-Aberth algorithm applying log-exp solution and the execution time of the Ehrlisch-Aberth algorithm without applying log-exp solution, with full polynomials degrees. We can see that the execution time for the both algorithms are the same while the polynomials degrees are less than 4500.After,we show clearly that the Ehrlisch-Aberth algorithm without applying log.exp stop to converge consequently,can not solving polynomial exceed 4500, in counterpart, applying log.exp solution the Ehrlisch-Aberth algorithm can solving very high and large full polynomial exceed 500,000 degrees.
+
+in fact, when the modulus of the roots are up than R given in (~\ref{eq:radiusR}),this exceed the the limited number in the mantissa of floating points representations who justify the divergence of the Ehrlisch-Aberth algorithm without log.exp. However, applying log.exp solution given in equation~\ref{alg3-update} took into account the limit of floating using the iterative function given in~\ref{eq:Aberth-H-GS}.
+
+
+
+%we report the performances of the exp.log for the Ehrlisch-Aberth algorithm for solving very high degree of polynomial. 
+
  
 \subsubsection{A comparative study between Aberth and Durand-kerner algorithm}
 
