Merge branch 'master' of ssh://info.iut-bm.univ-fcomte.fr/kahina_paper1

[kahina_paper1.git] / paper.tex

diff --git a/paper.tex b/paper.tex
index 5f12b9d8d60a3a24f26c610ed8c20b42b02bfbf3..5bef5e8cc9480aa580442e78b6644ab02b72181e 100644 (file)
--- 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}
 
 \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}   
 
 \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
 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
 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}
 
 
 \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
 
 \subsection{Background on the GPU architecture}
 A GPU is viewed as an accelerator for the data-parallel and