X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/blobdiff_plain/5b5a5f8b12045a82b01725b4d0de867b8b1123f2..8908949ea6e087603842b99d7548ea86f00d7d1f:/paper.tex

diff --git a/paper.tex b/paper.tex
index 5f12b9d..5bef5e8 100644
--- a/paper.tex
+++ b/paper.tex
@@ -333,7 +333,9 @@ Q(z_{k})=\exp\left( \ln (p(z_{k}))-\ln(p(z_{k}^{'}))+\ln \left(
 \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}   
@@ -359,7 +361,7 @@ parallelism that can be suitably exploited by SIMD machines.
 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
@@ -385,6 +387,8 @@ GPUs, which details are discussed in the sequel.
 
 
 \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