MAJ The comparative study

diff --git a/figures/EA_DK.pdf b/figures/EA_DK.pdf
index 5eb980829bce00777b3105f5491fcd948aca0002..69144ae1f91db330922568a4b3aa6209ef35f4f1 100644 (file)
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 dca073fd2f9267f998b79a3cda0485d8a05ba409..d3939a5a518a058d382df1702f87f135c6ce9cb2 100644 (file)
--- 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                      
 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
 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
 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
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diff --git a/paper.tex b/paper.tex
index 5bef5e8cc9480aa580442e78b6644ab02b72181e..35896aeff5ed485d271336c31dfbbf0bc59ef595 100644 (file)
--- 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:
 \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}
 $$R = \exp( \log(DBL\_MAX) / (2*n) )$$ 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}
 
 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.
 \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}
 
 
 \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}
 
 
 \subsubsection{Aberth algorithm on CPU and GPU}