X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/blobdiff_plain/e190c5da7c414d75199c2179a1d0268f4171c6c9..c18407ffc4e9394dd7573d81b3109ec0136dc7ce:/paper.tex?ds=inline

diff --git a/paper.tex b/paper.tex
index 34b803c..e1dfd58 100644
--- a/paper.tex
+++ b/paper.tex
@@ -583,7 +583,7 @@ Algorithm~\ref{alg2-cuda} shows a sketch of the Ehrlich-Aberth algorithm using C
 \caption{CUDA Algorithm to find roots with the Ehrlich-Aberth method}
 
 \KwIn{$Z^{0}$ (Initial root's vector), $\varepsilon$ (error tolerance
-  threshold), P(Polynomial to solve), Pu (the derivative of P), $n$ (Polynomial's degrees),$\Delta z_{max}$ (maximum value of stop condition)}
+  threshold), P(Polynomial to solve), Pu (the derivative of P), $n$ (Polynomial's degrees), $\Delta z_{max}$ (maximum value of stop condition)}
 
 \KwOut {$Z$ (The solution root's vector), $ZPrec$ (the previous solution root's vector)}
 
@@ -592,14 +592,14 @@ Algorithm~\ref{alg2-cuda} shows a sketch of the Ehrlich-Aberth algorithm using C
 Initialization of the of P\;
 Initialization of the of Pu\;
 Initialization of the solution vector $Z^{0}$\;
-Allocate and copy initial data to the GPU global memory ($d\_Z,d\_ZPrec,d\_P,d\_Pu$)\;
+Allocate and copy initial data to the GPU global memory\;
 k=0\;
 \While {$\Delta z_{max} > \epsilon$}{
  Let $\Delta z_{max}=0$\;
-$ kernel\_save(d\_ZPrec,d\_Z)$\;
+$ kernel\_save(ZPrec,Z)$\;
 k=k+1\;
-$ kernel\_update(d\_Z,d\_P,d\_Pu)$\;
-$kernel\_testConverge(\Delta z_{max},d\_Z,d\_ZPrec)$\;
+$ kernel\_update(Z,P,Pu)$\;
+$kernel\_testConverge(\Delta z_{max},Z,ZPrec)$\;
 
 }
 Copy results from GPU memory to CPU memory\;
@@ -619,10 +619,10 @@ exponential logarithm algorithm.
 %\LinesNumbered
 \caption{Kernel update}
 
-\eIf{$(\left|d\_Z\right|<= R)$}{
-$kernel\_update((d\_Z,d\_P,d\_Pu)$\;}
+\eIf{$(\left|Z\right|<= R)$}{
+$kernel\_update((Z,P,Pu)$\;}
 {
-$kernel\_update\_ExpoLog((d\_Z,d\_P,\_Pu))$\;
+$kernel\_update\_ExpoLog((Z,P,Pu))$\;
 }
 \end{algorithm}
 
@@ -772,6 +772,13 @@ methods on GPU. We took into account the execution time, the number of iteration
 \label{fig:04}
 \end{figure}
 
+\begin{figure}[htbp]
+\centering
+  \includegraphics[width=0.8\textwidth]{figures/EA_DK1}
+\caption{Execution times of the  Durand-Kerner and the Ehrlich-Aberth methods on GPU}
+\label{fig:0}
+\end{figure}
+
 Figure~\ref{fig:04} shows the execution times of both methods with
 sparse polynomial degrees ranging from 1,000 to 1,000,000. We can see
 that the Ehrlich-Aberth algorithm is faster than Durand-Kerner