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+\usepackage[utf8]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage[textsize=footnotesize]{todonotes}
+\newcommand{\LZK}[2][inline]{%
+ \todo[color=red!10,#1]{\sffamily\textbf{LZK:} #2}\xspace}
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\begin{document}
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% paper title
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-\title{A parallel implementation of Ehrlich-Aberth algorithm for root finding of polynomials
-on Multi-GPU with OpenMP/MPI}
+\title{Two parallel implementations of Ehrlich-Aberth algorithm for root finding of polynomials
+on multiple GPUs with OpenMP and MPI}
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\begin{abstract}
-The abstract goes here.
+\LZK{J'ai un peu modifié l'abstract. Sinon à revoir pour le degré max des polynômes testés après les tests de raph.}
+Finding roots of polynomials is a very important part of solving real-life problems but it is not so easy for polynomials of high degrees. In this paper, we present two different parallel algorithms of the Ehrlich-Aberth method to find roots of sparse and fully defined polynomials of high degrees. Both algorithms are based on CUDA technology to be implemented on multi-GPU computing platforms but each using different parallel paradigms: OpenMP or MPI. The experiments show a quasi-linear speedup by using up-to 4 GPU devices to find roots of polynomials of degree up-to 1.4 billion. To our knowledge, this is the first paper to present this technology mix to solve such a highly demanding problem in parallel programming. \LZK{Je n'ai pas bien saisi la dernière phrase.}
+
\end{abstract}
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