comment the figure 4

diff --git a/figures/EA_DK.txt b/figures/EA_DK.txt
index d3939a5a518a058d382df1702f87f135c6ce9cb2..0be66d1f1ef266ab5af4e64d2f3138560e83f27f 100644 (file)
--- a/figures/EA_DK.txt
+++ b/figures/EA_DK.txt
@@ -1,8 +1,8 @@
 # First data block (index 0)
 #EA            sparse                          full                                            
 #Taille_Poly   times           nb iter         times           nb iter                         
 # First data block (index 0)
 #EA            sparse                          full                                            
 #Taille_Poly   times           nb iter         times           nb iter                         

-5000           0.40            17
-50000          3.92            17              1407.24         29              
+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                      
 100000         12.45           16              1459.35         31                      
 150000          28.67          17              754.24          27                      
 200000         40              23              718.623         27                      


@@ -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             8.61        16
+5000           3.42            138             12.2491     186

 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/paper.tex b/paper.tex
index 7907494f1d577ecf3be95f67c24ca4a0c32b5034..76eab89355f6a4a1caa29812e73a08ea974d8b08 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -671,15 +671,15 @@ 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 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~\ref{Log_H1} ~\ref{Log_H2}.
+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. 

 
 
 
 %we report the performances of the exp.log for the Ehrlisch-Aberth algorithm for solving very high degree of polynomial. 
 
  
 
 
 
 %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}
-
+\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 

 
 \begin{figure}[H]
 \centering
 
 \begin{figure}[H]
 \centering