Modification de la figure 4....

diff --git a/figures/EA_DK.pdf b/figures/EA_DK.pdf
index 69144ae1f91db330922568a4b3aa6209ef35f4f1..95e4d8001e2b942069f606ac4984b19cf5153d9c 100644 (file)
Binary files a/figures/EA_DK.pdf and b/figures/EA_DK.pdf differ

diff --git a/figures/EA_DK.plot b/figures/EA_DK.plot
index 31436ba7ad9787d6a983b36efab2f60fb61e1141..c2ac5b8bf3c1ed18ad594aef1410fe5b68c82eee 100644 (file)
--- a/figures/EA_DK.plot
+++ b/figures/EA_DK.plot
@@ -6,12 +6,12 @@ set term postscript enhanced portrait "Helvetica" 12
 
 set ylabel "execution times (in s)" 
 set xlabel "polynomial's degree" 
 
 set ylabel "execution times (in s)" 
 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

-set style line 3 lc rgb '#dd181f' lt 1 lw 2 pt 1 ps 1.5   # --- red
+set style line 3 lc rgb '#dd181f' lt 1 lw 2 pt 2 ps 1.5   # --- red

 
 set style line 2 lc rgb '#dd181f' lt 1 lw 2 pt 5 ps 1.5   # --- red
 plot  'EA_DK.txt'index 0 using 1:2 t "EA with sparse polynomials"      with linespoints ls 1,\
 
 set style line 2 lc rgb '#dd181f' lt 1 lw 2 pt 5 ps 1.5   # --- red
 plot  'EA_DK.txt'index 0 using 1:2 t "EA with sparse polynomials"      with linespoints ls 1,\

diff --git a/figures/EA_DK.txt b/figures/EA_DK.txt
index 0be66d1f1ef266ab5af4e64d2f3138560e83f27f..5468c4c5f05d7fe994742ea7683530062b5a5b74 100644 (file)
--- a/figures/EA_DK.txt
+++ b/figures/EA_DK.txt
@@ -1,13 +1,13 @@
 # First data block (index 0)
 # First data block (index 0)

-#EA            sparse                          full                                            
+#EA            sparse                          full                                                                    

 #Taille_Poly   times           nb iter         times           nb iter                         
 5000           0.40            17              0.748784        25
 #Taille_Poly   times           nb iter         times           nb iter                         
 5000           0.40            17              0.748784        25

-50000          3.92            17              139.87          195             
-100000         12.45           16              1459.35         31                      
-150000          28.67          17              754.24          27                      
-200000         40              23              718.623         27                      
-250000         93.76           20              715.554         27                      
-300000         138.94          21              1089.61         27                      
+50000          3.92            17              25.9504         40              
+100000         12.45           16              54.5215         30                      
+150000          28.67          17              156.63          33                      
+200000         40              23              330.456         43                      
+250000         93.76           20              518.342         47                      
+300000         138.94          21              912.078         50                      

 350000         159.65          18              1746.53         22                      
 400000         258.91          22              3112            20                      
 450000         339.47          23              
 350000         159.65          18              1746.53         22                      
 400000         258.91          22              3112            20                      
 450000         339.47          23              

diff --git a/paper.tex b/paper.tex
index 76eab89355f6a4a1caa29812e73a08ea974d8b08..a72d1779e2de46874625a8f75decf67bbbd30972 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -671,7 +671,7 @@ In this experiment we report the performance of log.exp solution describe in ~\r
 
 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 classical version of Ehrlisch-Aberth algorithm (without applying log.exp) stop to converge and can not solving polynomial exceed 4500, in counterpart, the new version of Ehrlisch-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 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 classical version of Ehrlisch-Aberth algorithm (without applying log.exp) stop to converge and can not solving polynomial exceed 4500, in counterpart, the new version of Ehrlisch-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 Ehrlisch-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 Ehrlisch-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 . 

 
 
 
 
 
 


@@ -679,15 +679,17 @@ in fact, when the modulus of the roots are up than \textit{R} given in ~\ref{R},
 
  
 \subsubsection{A comparative study between Ehrlisch-Aberth algorithm and Durand-kerner algorithm}
 
  
 \subsubsection{A comparative study between Ehrlisch-Aberth algorithm and Durand-kerner algorithm}

-In this part, we are interesting to compare the simultaneous methods, Ehrlisch-Aberth and Durand-Kerner in parallel computer using GPU. We took into account the execution time, the number of iteration and the polynomials size 
+In this part, we are interesting to compare the simultaneous methods, Ehrlisch-Aberth and Durand-Kerner in parallel computer using GPU. We took into account the execution time, the number of iteration and the polynomial's size. for the both sparse and full polynomials.  

 
 \begin{figure}[H]
 \centering
   \includegraphics[width=0.8\textwidth]{figures/EA_DK}
 
 \begin{figure}[H]
 \centering
   \includegraphics[width=0.8\textwidth]{figures/EA_DK}

-\caption{The execution time of Ehrlisch-Aberth versus Durand-Kerner algorithm}
+\caption{The execution time of Ehrlisch-Aberth versus Durand-Kerner algorithm on GPU}

 \label{fig:01}
 \end{figure}
 
 \label{fig:01}
 \end{figure}
 

+This figure show the execution time of the both algorithm EA and DK with sparse polynomial degrees ranging from 1000 to 1000000. We can see that the Ehrlisch-Aberth algorithm are faster than Durand-Kerner algorithm, with an average of 25 times as fast. Then, when degrees of polynomial exceed 500000 the execution time with EA is of the order 100 whereas DK passes in the order 1000. %with double precision not exceed $10^{-5}$.
+

 \begin{figure}[H]
 \centering
   \includegraphics[width=0.8\textwidth]{figures/EA_DK_nbr}
 \begin{figure}[H]
 \centering
   \includegraphics[width=0.8\textwidth]{figures/EA_DK_nbr}