--- /dev/null
+# Analysis description
+set encoding iso_8859_1
+set terminal x11
+set size 1,0.5
+set term postscript enhanced portrait "Helvetica" 12
+
+set ylabel "execution times (in s)"
+set xlabel "Sparse and full polynomial's degrees"
+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 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 "Sparse polynomial No log.exp" with linespoints ls 2,\
+ 'log_exp_Sparse.txt' index 0 using 1:2 t "Sparse polynomial with log.exp" with linespoints ls 1,\
+ 'log_exp_Sparse.txt' index 1 using 1:2 t "Sparse polynomial with log.exp" with linespoints ls 1,\
+'log_exp.txt' index 0 using 1:4 t "Full polynomial No log.exp" with linespoints ls 2,\
+ 'log_exp.txt' index 0 using 1:2 t "Full polynomial with log.exp" with linespoints ls 1,\
+ 'log_exp.txt'index 1 using 1:2 t "Full polynomail withlog.exp" with linespoints ls 1
\ No newline at end of file
--- /dev/null
+#sparse polynomial
+# First data block (index 0)
+#EA With_log_exp No_log_exp
+#Taille_Poly times nb iter times nb iter
+5000 0.289431 17 0.256983 15
+10000 0.319229 14 0.317802 14
+15000 0.317802 14 0.393191 13
+25000 0.759156 11 0.849403 11
+30000 1.26306 16 2.08251 20
+40000 2.57116 19 2.58756 18
+50000 4.17865 18 4.80419 20
+60000 4.43633 16 4.92617 17
+100000 11.7038 15 12.4761 16
+150000 18.6746 11 16.3098 16
+
+# Second index block (index 1)
+#Taille_Poly times nb iter
+150000 18.6746 11
+200000 67.6199 22
+300000 132.27 20
+350000 159.65 18
+400000 258.91 22
+450000 339.47 23
+500000 419.78 23
+550000 415.94 19
+600000 549.70 21
+650000 612.12 20
+700000 864.21 24
+750000 940.87 23
+800000 1247.16 26
+850000 1702.12 32
+900000 1803.17 30
+950000 2280.07 34
+1000000 2400.51 30
+
+#Full polynomial
+# First data block (index 2)
+#EA With_log_exp No_log_exp
+#Taille_Poly times nb iter times nb iter
+500 0.224633 16 0.23799 17
+1000 0.348493 24 0.36104 24
+1500 0.337472 21 0.339825 20
+2000 0.36503 21 0.389243 21
+2500 0.389436 22 0.438976 27
+3000 0.404811 20 0.403387 27
+3500 0.487981 21 0.490296 22
+4000 0.506183 23 0.550917 20
+
+# Second index block (index 3)
+#EA With_log_exp
+#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
+100000 306.117 141
+
+
In this experiment we report the performance of log.exp solution describe in ~\ref{sec2} to compute very high degrees polynomials.
\begin{figure}[H]
\centering
- \includegraphics[width=0.8\textwidth]{figures/log_exp}
+ \includegraphics[width=0.8\textwidth]{figures/sparse_full_explog}
\caption{The impact of exp-log solution to compute very high degrees of polynomial.}
\label{fig:01}
\end{figure}
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}
+%\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.
