MAJ du commentaire de la figure log.exp with sparse and full poly....

diff --git a/figures/EA_DK.txt b/figures/EA_DK.txt
index 3ff0845ee9adb010af665ac838dd6815f6332d16..187bb3a690d480a5583334caaece5f869a4b341a 100644 (file)
--- a/figures/EA_DK.txt
+++ b/figures/EA_DK.txt
@@ -27,7 +27,7 @@
 
 #DK            sparse                          full                                    
                times           nb iter         times       nb iter             
 
 #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
 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 dd56d0309628dad14378c3e8c81127cec2976b11..e507d320583d170307d90898e3612c72c8f9c69b 100644 (file)
--- 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 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
 
 #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 1ba7a17a41ed19786a7f6f92f03f65279dd84512..5cc9bdff518e1513e51aa40e8462f889e90e79da 100644 (file)
--- 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}
 
 \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 . 
 
 
 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 .