MAJ de quelque figures

diff --git a/figures/EA_DK.pdf b/figures/EA_DK.pdf
index 95e4d8001e2b942069f606ac4984b19cf5153d9c..f992927f22752539856d3fbcaddb9c5f08199899 100644 (file)
Binary files a/figures/EA_DK.pdf and b/figures/EA_DK.pdf differ

diff --git a/figures/log_exp.pdf b/figures/log_exp.pdf
index 2ccdbf64daaa02dafa56ce8fb28be75e4526a33d..900ebc033e6ba24526ac4dc112a591a1f9a2b887 100644 (file)
Binary files a/figures/log_exp.pdf and b/figures/log_exp.pdf differ

diff --git a/figures/log_exp.plot b/figures/log_exp.plot
index a1ba5d8e8bdb345620b58a0a92888fb914b661a6..edd5ab1d16f1a23b9b05890a30594c2083c1211a 100644 (file)
--- a/figures/log_exp.plot
+++ b/figures/log_exp.plot
@@ -14,5 +14,5 @@ set style line 1 lc rgb '#0060ad' lt 1 lw 2 pt 1 ps 1.5   # --- blue
 set style line 2 lc rgb '#dd181f' lt 1 lw 2 pt 5 ps 1.5   # --- red
 
   plot'log_exp.txt' index 0 using 1:4 t "No log exp"       with linespoints ls 2,\
 set style line 2 lc rgb '#dd181f' lt 1 lw 2 pt 5 ps 1.5   # --- red
 
   plot'log_exp.txt' index 0 using 1:4 t "No log exp"       with linespoints ls 2,\

- 'log_exp.txt' index 0 using 1:2 t "with log exp"      with linespoints ls 1,\
- 'log_exp.txt'index 1 using 1:2 t "with_log_exp"      with linespoints ls 1
+ 'log_exp.txt' index 0 using 1:2 t "with log exp"         with linespoints ls 1,\
+ 'log_exp.txt'index 1 using 1:2 t "with_log_exp"          with linespoints ls 1

diff --git a/figures/log_exp.txt b/figures/log_exp.txt
index 47874d7c30cce87f686c45c49c1bbd10cbe28aed..afe212b7af6e51856fb36869a54879acaa3001fc 100644 (file)
--- a/figures/log_exp.txt
+++ b/figures/log_exp.txt
@@ -13,8 +13,9 @@
 
 # Second index block (index 1)
 #EA            With_log_exp
 
 # Second index block (index 1)
 #EA            With_log_exp

-#Taille_Poly   times           nb iter                         
-4500           0.946749        23
+#Taille_Poly   times           nb iter
+4000           0.506183        23                              
+#4500          0.946749        23

 5000           0.769945        33
 6000           1.38447         48
 10000          2.15026         32
 5000           0.769945        33
 6000           1.38447         48
 10000          2.15026         32

diff --git a/figures/log_exp_Sparse.pdf b/figures/log_exp_Sparse.pdf
new file mode 100644 (file)
index 0000000..e2315a7
Binary files /dev/null and b/figures/log_exp_Sparse.pdf differ

diff --git a/figures/log_exp_Sparse.plot b/figures/log_exp_Sparse.plot
index 21c9fb73faf66533010385c44c54c89e8df78e02..e9acccf5bca94670dd73183ed9b8fcdd66abe68a 100644 (file)
--- a/figures/log_exp_Sparse.plot
+++ b/figures/log_exp_Sparse.plot
@@ -5,7 +5,7 @@ set size 1,0.5
 set term postscript enhanced portrait "Helvetica" 12
 
 set ylabel "execution times (in s)" 
 set term postscript enhanced portrait "Helvetica" 12
 
 set ylabel "execution times (in s)" 

-set xlabel "Soarse polynomial's degrees" 
+set xlabel "Sparse polynomial's degrees" 

 set logscale x
 set logscale y
 
 set logscale x
 set logscale y
 


@@ -15,4 +15,4 @@ set style line 2 lc rgb '#dd181f' lt 1 lw 2 pt 5 ps 1.5   # --- red
 
   plot'log_exp_Sparse.txt' index 0 using 1:4 t "No log exp"       with linespoints ls 2,\
  'log_exp_Sparse.txt' index 0 using 1:2 t "with log exp"      with linespoints ls 1,\
 
   plot'log_exp_Sparse.txt' index 0 using 1:4 t "No log exp"       with linespoints ls 2,\
  'log_exp_Sparse.txt' index 0 using 1:2 t "with log exp"      with linespoints ls 1,\

- 'log_exp_Sparse.txt'index 1 using 1:2 t "with_log_exp"      with linespoints ls 1
\ No newline at end of file
+ 'log_exp_Sparse.txt' index 1 using 1:2 t "with_log_exp"      with linespoints ls 1
\ No newline at end of file

diff --git a/figures/log_exp_Sparse.txt b/figures/log_exp_Sparse.txt
index aa2cff5135ba1e68e4ac7f7c9756c818234d1699..0dc90fce632315d4b0135a26132b961b188cf4d9 100644 (file)
--- a/figures/log_exp_Sparse.txt
+++ b/figures/log_exp_Sparse.txt
@@ -14,7 +14,8 @@
 150000         18.6746         11              16.3098         16
 
 # Second index block (index 1)
 150000         18.6746         11              16.3098         16
 
 # Second index block (index 1)

-#Taille_Poly   times           nb iter                         
+#Taille_Poly   times           nb iter
+150000         18.6746         11                              

 200000         67.6199         22
 300000         132.27          20
 350000         159.65          18                              
 200000         67.6199         22
 300000         132.27          20
 350000         159.65          18                              

diff --git a/paper.tex b/paper.tex
index 4ce9747f5e6d9bddf5ddea2fb4f842d08b068ccb..c12aeda99cb2c577b87e07c042a188fccd83e50e 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -672,6 +672,12 @@ The figure 3, show a comparison between the execution time of the Ehrlich-Aberth
 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 . 
 
 

+\begin{figure}[H]
+\centering
+  \includegraphics[width=0.8\textwidth]{figures/log_exp_Sparse}
+\caption{The impact of exp-log solution to compute very high degrees of  polynomial.}
+\label{fig:01}
+\end{figure}

 
 %we report the performances of the exp.log for the Ehrlich-Aberth algorithm for solving very high degree of polynomial. 
 
 
 %we report the performances of the exp.log for the Ehrlich-Aberth algorithm for solving very high degree of polynomial.