From: Kahina <kahina@kahina-VPCEH3K1E.(none)>
Date: Mon, 26 Oct 2015 12:30:42 +0000 (+0100)
Subject: comment the figure 4
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/commitdiff_plain/9db987b1a9ab69bedb939fc8f49605c11d18f7b5?ds=sidebyside
comment the figure 4
---
diff --git a/figures/EA_DK.txt b/figures/EA_DK.txt
index d3939a5..0be66d1 100644
--- 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
-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
@@ -27,7 +27,7 @@
#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
diff --git a/paper.tex b/paper.tex
index 7907494..76eab89 100644
--- 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.
-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.
-\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