From: Kahina Date: Fri, 23 Oct 2015 12:59:38 +0000 (+0200) Subject: MAJ figure 4 X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/commitdiff_plain/c5e1141650462fe452663bbf018f1c136914de28?ds=inline MAJ figure 4 et quelques remarques faites par SIDER --- diff --git a/figures/EA_DK.pdf b/figures/EA_DK.pdf index 732fb08..5eb9808 100644 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 e20822a..dca073f 100644 --- 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 b9ed2ff..02f98de 100644 --- 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