From: Kahina Date: Tue, 27 Oct 2015 10:34:00 +0000 (+0100) Subject: MAJ du commentaire de la figure log.exp with sparse and full poly.... X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/commitdiff_plain/47a5fd428748f325685f04bda4145dad7efa49e3?ds=sidebyside;hp=-c MAJ du commentaire de la figure log.exp with sparse and full poly.... --- 47a5fd428748f325685f04bda4145dad7efa49e3 diff --git a/figures/EA_DK.txt b/figures/EA_DK.txt index 3ff0845..187bb3a 100644 --- a/figures/EA_DK.txt +++ b/figures/EA_DK.txt @@ -27,7 +27,7 @@ #DK sparse full times nb iter times nb iter -5000 3.42 138 12.2491 186 +5000 3.42 138 638.572 9597 50000 385.266 823 9.27 19 100000 447.364 408 7.73 15 150000 1524.08 552 8.64 21 diff --git a/figures/EA_DK_nbr.plot b/figures/EA_DK_nbr.plot index dd56d03..e507d32 100644 --- a/figures/EA_DK_nbr.plot +++ b/figures/EA_DK_nbr.plot @@ -6,8 +6,8 @@ set term postscript enhanced portrait "Helvetica" 12 set ylabel "number of iterations" set xlabel "polynomial's degree" -set logscale x -set logscale y +#set logscale x +#set logscale y #set key on outside left bmargin set style line 1 lc rgb '#0060ad' lt 1 lw 2 pt 1 ps 1.5 # --- blue diff --git a/paper.tex b/paper.tex index 1ba7a17..5cc9bdf 100644 --- a/paper.tex +++ b/paper.tex @@ -667,7 +667,7 @@ In this experiment we report the performance of log.exp solution describe in ~\r \label{fig:01} \end{figure} -The figure 3, show a comparison between the execution time of the Ehrlich-Aberth algorithm applying log-exp solution and the execution time of the Ehrlich-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 classical version of Ehrlich-Aberth algorithm (without applying log.exp) stop to converge and can not solving polynomial exceed 4500, in counterpart, the new version of Ehrlich-Aberth algorithm (applying log.exp solution) can solve very high and large full polynomial exceed 100,000 degrees. +The figure 3, show a comparison between the execution time of the Ehrlich-Aberth algorithm applying log-exp solution and the execution time of the Ehrlich-Aberth algorithm without applying log-exp solution, with full and sparse polynomials degrees. We can see that the execution time for the both algorithms are the same while the full polynomials degrees are less than 4000 and full polynomials are less than 150,000. After,we show clearly that the classical version of Ehrlich-Aberth algorithm (without applying log.exp) stop to converge and can not solving any polynomial sparse or full. In counterpart, the new version of Ehrlich-Aberth algorithm (applying log.exp solution) can solve very high and large full polynomial exceed 100,000 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 .