From 6406a4635cdffc93164ba02af83fbb25b17a56f0 Mon Sep 17 00:00:00 2001
From: couturie <raphael.couturier@univ-fcomte.Fr>
Date: Tue, 20 Oct 2015 13:29:43 +0200
Subject: [PATCH] new

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-  \def\href#1#2{#2} \def\path#1{#1}\fi
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-\bibitem{Weierstrass03}
-K.~Weierstrass, Neuer beweis des satzes, dass jede ganze rationale function
-  einer veranderlichen dagestellt werden kann als ein product aus linearen
-  functionen derselben veranderlichen, Ges. Werke 3 (1903) 251--269.
-
-\bibitem{Ilie50}
-L.~Ilieff, On the approximations of newton, Annual Sofia Univ~(46) (1950)
-  167--171.
-\newblock \href {http://dx.doi.org/10.1016/0003-4916(63)90068-X}
-  {\path{doi:10.1016/0003-4916(63)90068-X}}.
-
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-  the roots of a given algebraic equation, Phys. Math. J~(5) (1962) 136--139.
-
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-E.~Durand, Solution numerique des equations algebriques, vol. 1, equations du
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-O.~Aberth, Iteration methods for finding all zeros of a polynomial
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-  advanced Networking, Distributed Systems and Applications (2014) 53--57.
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-  Numerical Algorithms 13~(4) (1996) 179--200.
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-  polynomial zeroes, Proc of the 6th int conference on advance computing, CDAC,
-  Pune University Campus,India 15~(3) (1999) 189--196.
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-  a ring multicomputer, Clust Comput 2~(10) (2007) 167--174.
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-
-\end{thebibliography}
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-\BOOKMARK [1][-]{section.1}{Root finding problem}{}% 1
-\BOOKMARK [1][-]{section.2}{Aberth method}{}% 2
-\BOOKMARK [2][-]{subsection.2.1}{Polynomials Initialization}{section.2}% 3
-\BOOKMARK [2][-]{subsection.2.2}{Vector Z\(0\) Initialization}{section.2}% 4
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-\BOOKMARK [2][-]{subsection.2.4}{Convergence condition}{section.2}% 6
-\BOOKMARK [1][-]{section.3}{Amelioration of Aberth method }{}% 7
-\BOOKMARK [1][-]{section.4}{The implementation of simultaneous methods in a parallel computer}{}% 8
-\BOOKMARK [1][-]{section.5}{A parallel implementation of Aberth method}{}% 9
-\BOOKMARK [2][-]{subsection.5.1}{Background on the GPU architecture}{section.5}% 10
-\BOOKMARK [2][-]{subsection.5.2}{Background on the CUDA Programming Model}{section.5}% 11
-\BOOKMARK [2][-]{subsection.5.3}{ The implementation of Aberth method on GPU}{section.5}% 12
-\BOOKMARK [3][-]{subsubsection.5.3.1}{A sequential Aberth algorithm}{subsection.5.3}% 13
-\BOOKMARK [3][-]{subsubsection.5.3.2}{Parallelize the steps on GPU }{subsection.5.3}% 14
-\BOOKMARK [2][-]{subsection.5.4}{Experimental study}{section.5}% 15
-\BOOKMARK [3][-]{subsubsection.5.4.1}{Definition of the polynomial used}{subsection.5.4}% 16
-\BOOKMARK [3][-]{subsubsection.5.4.2}{The study condition}{subsection.5.4}% 17
-\BOOKMARK [3][-]{subsubsection.5.4.3}{Comparative study}{subsection.5.4}% 18
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2.39.5