From: Kahina <kahina@kahina-VPCEH3K1E.(none)>
Date: Sat, 24 Oct 2015 23:30:55 +0000 (+0200)
Subject: MAJ The comparative study
X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/commitdiff_plain/d5a8b20ef4abd7e732263bfc285709b72885d259?ds=sidebyside;hp=--cc

MAJ The comparative study
---

d5a8b20ef4abd7e732263bfc285709b72885d259
diff --git a/figures/EA_DK.pdf b/figures/EA_DK.pdf
index 5eb9808..69144ae 100644
Binary files a/figures/EA_DK.pdf and b/figures/EA_DK.pdf differ
diff --git a/figures/EA_DK.txt b/figures/EA_DK.txt
index dca073f..d3939a5 100644
--- a/figures/EA_DK.txt
+++ b/figures/EA_DK.txt
@@ -10,7 +10,7 @@
 300000		138.94		21		1089.61		27			
 350000		159.65		18		1746.53		22			
 400000		258.91		22 		3112		20			
-450000		339.47		23
+450000		339.47		23		
 500000		419.78		23
 550000		415.94		19
 600000		549.70		21
@@ -35,12 +35,12 @@
 250000		1958.24		348		11.33	    18
 300000		2800.53 	319		20.47	    21
 350000		4071.47		378		35.07	    26
-400000
-450000
-500000
-550000
-600000
-650000
+400000		3339.4		238
+450000		3983.34		221
+500000		5737.84 	257
+550000		6783.73		235
+600000		12339 		398
+650000		
 700000
 750000
 800000
diff --git a/paper.tex b/paper.tex
index 5bef5e8..35896ae 100644
--- a/paper.tex
+++ b/paper.tex
@@ -334,7 +334,6 @@ Q(z_{k})=\exp\left( \ln (p(z_{k}))-\ln(p(z_{k}^{'}))+\ln \left(
 \end{equation}
 
 This solution is applied when the root except the circle unit, represented by the radius $R$ evaluated as:
-
 $$R = \exp( \log(DBL\_MAX) / (2*n) )$$ where $DBL\_MAX$ stands for the maximum representable double value.
 
 \section{The implementation of simultaneous methods in a parallel computer}
@@ -493,7 +492,7 @@ There exists two ways to execute the iterative function that we call a Jacobi on
 H(i,z^{k+1})=\frac{p(z^{(k)}_{i})}{p'(z^{(k)}_{i})-p(z^{(k)}_{i})\sum^{n}_{j=1 j\neq i}\frac{1}{z^{(k)}_{i}-z^{(k)}_{j}}}, i=1,...,n.
 \end{equation}
 
-With the the Gauss-seidel iteration, we have:
+With the Gauss-seidel iteration, we have:
 \begin{equation}
 \label{eq:Aberth-H-GS}
 H(i,z^{k+1})=\frac{p(z^{(k)}_{i})}{p'(z^{(k)}_{i})-p(z^{(k)}_{i})(\sum^{i-1}_{j=1}\frac{1}{z^{(k)}_{i}-z^{(k+1)}_{j}}+\sum^{n}_{j=i+1}\frac{1}{z^{(k)}_{i}-z^{(k)}_{j}})}, i=1,...,n.
@@ -622,7 +621,11 @@ E5620@2.40GHz and a GPU K40 (with 6 Go of ram).
 
 
 \subsection{Comparative study}
-We initially carried out the convergence of Aberth algorithm with various sizes of polynomial, in second we evaluate the influence of the size of the threads per block....
+In this section, we discuss the performance Ehrlish-Aberth method  of root finding polynomials implemented on CPUs and on GPUs.
+
+We performed a set of experiments on the sequential and the parallel algorithms, for both sparse and full polynomials and different sizes. We took into account the execution time,the  polynomial size and the number of threads per block performed by sum or each experiment on CPUs and on GPUs.
+
+All experimental results obtained from the simulations are made in double precision data, for a convergence tolerance of the methods set to $10^{-7}$. Since we were more interested in the comparison of the performance behaviors of Ehrlish-Aberth and Durand-Kerner methods on CPUs versus on GPUs.
 
 \subsubsection{Aberth algorithm on CPU and GPU}