\sum_{k\neq j}^{n}\frac{1}{z_{k}-z_{j}}\right)\right).
\end{equation}
-This solution is applied when it is necessary ??? When ??? (SIDER)
+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}
\label{secStateofArt}
Moreover, they have fast rate of convergence (quadratic for the
Durand-Kerner and cubic for the Ehrlisch-Aberth). Various parallel
algorithms reported for these methods can be found
-in~\cite{Cosnard90, Freeman89,Freemanall90,,Jana99,Janall99}.
+in~\cite{Cosnard90, Freeman89,Freemanall90,Jana99,Janall99}.
Freeman and Bane~\cite{Freemanall90} presented two parallel
algorithms on a local memory MIMD computer with the compute-to
communication time ratio O(n). However, their algorithms require
\section {A CUDA parallel Ehrlisch-Aberth method}
+In the following, we describe the parallel implementation of Ehrlisch-Aberth method on GPU
+for solving high degree polynomials. First, the hardware and software of the GPUs are presented. Then, a CUDA parallel Ehrlisch-Aberth method are presented.
\subsection{Background on the GPU architecture}
A GPU is viewed as an accelerator for the data-parallel and
