\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
\BOOKMARK [2][-]{subsection.2.3}{Iterative Function Hi}{section.2}% 5
\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