+In the previuos section we saw that both approches are very effective in reducing execution time for sparse as well as full polynomials. At this stage, the interesting question is which approach is better. In the fellowing, we present appropriate experiments comparing the two Multi-GPU approaches to answer the question.
+
+\subsubsection{Solving sparse polynomials}
+In this experiment three sparse polynomials of size 200K, 800K and 1,4M are investigated.
+\begin{figure}[htbp]
+\centering
+ \includegraphics[angle=-90,width=0.5\textwidth]{Sparse}
+\caption{Execution time for solving sparse polynomials of three distinct sizes on multiple GPUs using MPI and OpenMP approaches using Ehrlich-Aberth}
+\label{fig:05}
+\end{figure}
+In Figure~\ref{fig:05} there two curves for each polynomial size : one for the MPI-CUDA and another for the OpenMP. We can see that the results are similar between OpenMP and MPI for the polynomials size of 200K. For the size of 800K, the MPI version is a little slower than the OpenMP approach but for for the 1,4M size, there is a slight advantage for the MPI version.
+
+\subsubsection{Solving full polynomials}
+\begin{figure}[htbp]
+\centering
+ \includegraphics[angle=-90,width=0.5\textwidth]{Full}
+\caption{Execution time for solving full polynomials of three distinct sizes on multiple GPUs using MPI and OpenMP approaches using Ehrlich-Aberth}
+\label{fig:06}
+\end{figure}
+In Figure~\ref{fig:06}, we can see that when it comes to full polynomials, both approaches are almost equivalent.
+
+\subsubsection{Solving sparse and full polynomials of the same size with CUDA-MPI}
+In this experiment we compare the execution time of the EA algorithm according to the number of GPUs for solving sparse and full polynomials on Multi-GPU using MPI. We chose three sparse and full polynomials of size 200K, 800K and 1,4M.
+\begin{figure}[htbp]
+\centering
+ \includegraphics[angle=-90,width=0.5\textwidth]{MPI}
+\caption{Execution time for solving sparse and full polynomials of three distinct sizes on multiple GPUs using MPI}
+\label{fig:07}
+\end{figure}
+in figure ~\ref{fig:07} we can see that CUDA-MPI can solve sparse and full polynomials of high degrees, the execution time with sparse polynomial are very low comparing to full polynomials. with sparse polynomials the number of monomial are reduce, consequently the number of operation are reduce than the execution time decrease.
+
+\subsubsection{Solving sparse and full polynomials of the same size with CUDA-OpenMP}
+
+\begin{figure}[htbp]
+\centering
+ \includegraphics[angle=-90,width=0.5\textwidth]{OMP}
+\caption{Execution time for solving sparse and full polynomials of three distinct sizes on multiple GPUs using OpenMP}
+\label{fig:08}
+\end{figure}
+
+Figure ~\ref{fig:08} shows the impact of sparsity on the effectiveness of the CUDA-OpenMP approach. We can see that the impact fellows the same pattern, a difference in execution time in favor of the sparse polynomials.
+%SIDER : il faut une explication ici. je ne vois pas de prime abords, qu'est-ce qui engendre cette différence, car quelques soient les coefficients nulls ou non nulls, c'est toutes les racines qui sont calculées qu'elles soient similaires ou non (degrés de multiplicité).
+\subsection{Scalability of the EA method on Multi-GPU to solve very high degree polynomials}
+These experiments report the execution time according to the degrees of polynomials ranging from 1,000,000 to 5,000,000 for both approaches with sparse and full polynomials.
+\begin{figure}[htbp]
+\centering
+ \includegraphics[angle=-90,width=0.5\textwidth]{big}
+ \caption{Execution times in seconds of the Ehrlich-Aberth method for solving full polynomials of high degree on 4 GPUs for sizes ranging from 1M to 5M}
+\label{fig:09}
+\end{figure}
+In figure ~\ref{fig:09} we can see that both approaches are scalable and can solve very high degree polynomials. With full polynomial both approaches give interestingly very similar results. For the sparse case however, there are a noticeable difference in favour of MPI when the degree is above 4M. Between 1M and 3M, the OMP approach is more effective and under 1M degree, OMP and MPI approaches are almost equivalent.
+
+%SIDER : il faut une explication sur les différences ici aussi.
+
+%for sparse and full polynomials
