MAJ figure 4

et quelques remarques faites par SIDER

diff --git a/figures/EA_DK.pdf b/figures/EA_DK.pdf
index 732fb08bea92ed5762845ea7bb2f77e448c06752..5eb980829bce00777b3105f5491fcd948aca0002 100644 (file)
Binary files a/figures/EA_DK.pdf and b/figures/EA_DK.pdf differ

diff --git a/figures/EA_DK.txt b/figures/EA_DK.txt
index e20822ae2e39e39f51277767199e6c711bcbed85..dca073fd2f9267f998b79a3cda0485d8a05ba409 100644 (file)
--- a/figures/EA_DK.txt
+++ b/figures/EA_DK.txt
@@ -31,10 +31,10 @@
 50000          385.266         823             9.27        19
 100000         447.364         408             7.73        15
 150000         1524.08         552             8.64        21
-200000         3.92233         17              7.84        16
+200000         1530.86         360             7.84        16
 250000         1958.24         348             11.33       18
-300000         12.3981         21              20.47       21
-350000         23.813          21              35.07       26
+300000         2800.53         319             20.47       21
+350000         4071.47         378             35.07       26
 400000
 450000
 500000

diff --git a/paper.tex b/paper.tex
index b9ed2ff086ce48a77d9b05c9f11ab746923e3a48..02f98de83b7777e248bb3e8e5abe2441e3e5cbd9 100644 (file)
--- a/paper.tex
+++ b/paper.tex
@@ -330,7 +330,9 @@ 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}   
@@ -356,7 +358,7 @@ 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
@@ -382,6 +384,8 @@ 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