\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\bibstyle{elsarticle-num}
\emailauthor{kahina.ghidouche@gmail.com}{Ghidouche Kahina\corref {mycorrespondingauthor}}
\emailauthor{raphael.couturier@univ-fcomte.fr}{Couturier Raphael\corref {mycorrespondingauthor}}
\emailauthor{ar.sider@univ-bejaia.dz}{Abderrahmane Sider\corref {mycorrespondingauthor}}
\Newlabel{mycorrespondingauthor}{1}
\Newlabel{myfootnote}{1}
\Newlabel{mymainaddress}{a}
\Newlabel{mysecondaryaddress}{b}
\@writefile{toc}{\contentsline {section}{\numberline {1}Root finding problem}{1}{section.1}}
\citation{Weierstrass03}
\citation{Ilie50}
\citation{Docev62}
\citation{Durand60}
\citation{Kerner66}
\citation{Borch-Supan63}
\citation{Ehrlich67}
\citation{Aberth73}
\citation{Loizon83}
\citation{Freeman89}
\citation{Loizon83}
\citation{Freemanall90}
\citation{Raphaelall01}
\citation{CUDA10}
\citation{Kahinall14}
\@writefile{toc}{\contentsline {paragraph}{}{3}{section*.1}}
\citation{Aberth73}
\citation{Weierstrass03}
\citation{Aberth73}
\citation{Bini96}
\citation{Ostrowski41}
\@writefile{toc}{\contentsline {section}{\numberline {2}Aberth method}{4}{section.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Polynomials Initialization}{4}{subsection.2.1}}
\citation{Karimall98}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Vector $Z^{(0)}$ Initialization}{5}{subsection.2.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Iterative Function $H_{i}$}{5}{subsection.2.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Convergence condition}{5}{subsection.2.4}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Amelioration of Aberth method }{5}{section.3}}
\citation{Karimall98}
\citation{Mirankar68,Mirankar71}
\citation{Schedler72}
\citation{Winogard72}
\citation{Benall68,Jana06,Janall99,Riceall06}
\citation{Azad07,Gemignani07,Kalantari08,Skachek08,Zhancall08,Zhuall08}
\citation{Bini04}
\citation{Cosnard90,Freeman89,Freemanall90,,Jana99,Janall99}
\citation{Freemanall90}
\citation{Mirankar71}
\@writefile{toc}{\contentsline {section}{\numberline {4}The implementation of simultaneous methods in a parallel computer}{6}{section.4}}
\citation{Kahinall14}
\citation{NVIDIA10}
\@writefile{toc}{\contentsline {section}{\numberline {5}A parallel implementation of Aberth method}{8}{section.5}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Background on the GPU architecture}{8}{subsection.5.1}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Background on the CUDA Programming Model}{9}{subsection.5.2}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.3} The implementation of Aberth method on GPU}{10}{subsection.5.3}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.3.1}A sequential Aberth algorithm}{10}{subsubsection.5.3.1}}
\@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces Algorithm to find root polynomial with Aberth method}}{10}{algocf.1}}
\@writefile{toc}{\contentsline {paragraph}{The execution time}{11}{section*.2}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.3.2}Parallelize the steps on GPU }{12}{subsubsection.5.3.2}}
\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces Algorithm to find root polynomial with Aberth method}}{13}{algocf.2}}
\@writefile{loa}{\contentsline {algocf}{\numberline {3}{\ignorespaces A global Algorithm for the iterative function}}{14}{algocf.3}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Experimental study}{14}{subsection.5.4}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.4.1}Definition of the polynomial used}{14}{subsubsection.5.4.1}}
\bibdata{mybibfile}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.4.2}The study condition}{15}{subsubsection.5.4.2}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.4.3}Comparative study}{15}{subsubsection.5.4.3}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces the convergence of Aberth algorithm}}{15}{table.1}}
\newlabel{tab:theConvergenceOfAberthAlgorithm}{{1}{15}{the convergence of Aberth algorithm}{table.1}{}}
\@writefile{toc}{\contentsline {paragraph}{Aberth algorithm on CPU and GPU}{15}{table.1}}
\@writefile{toc}{\contentsline {paragraph}{The impact of the thread's number into the convergence of Aberth algorithm}{15}{table.2}}
\bibcite{Weierstrass03}{{1}{}{{}}{{}}}
\bibcite{Ilie50}{{2}{}{{}}{{}}}
\bibcite{Docev62}{{3}{}{{}}{{}}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces The impact of the thread's number into the convergence of Aberth algorithm}}{16}{table.2}}
\newlabel{tab:Theimpactofthethread'snumberintotheconvergenceofAberthalgorithm}{{2}{16}{The impact of the thread's number into the convergence of Aberth algorithm}{table.2}{}}
\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Aberth algorithm compare to Durand-Kerner algorithm}}{16}{table.3}}
\newlabel{tab:AberthAlgorithCompareToDurandKernerAlgorithm}{{3}{16}{Aberth algorithm compare to Durand-Kerner algorithm}{table.3}{}}
\@writefile{toc}{\contentsline {paragraph}{A comparative study between Aberth and Durand-kerner algorithm}{16}{table.3}}
\bibcite{Durand60}{{4}{}{{}}{{}}}
\bibcite{Kerner66}{{5}{}{{}}{{}}}
\bibcite{Borch-Supan63}{{6}{}{{}}{{}}}
\bibcite{Ehrlich67}{{7}{}{{}}{{}}}
\bibcite{Aberth73}{{8}{}{{}}{{}}}
\bibcite{Loizon83}{{9}{}{{}}{{}}}
\bibcite{Freeman89}{{10}{}{{}}{{}}}
\bibcite{Freemanall90}{{11}{}{{}}{{}}}
\bibcite{Raphaelall01}{{12}{}{{}}{{}}}
\bibcite{CUDA10}{{13}{}{{}}{{}}}
\bibcite{Kahinall14}{{14}{}{{}}{{}}}
\bibcite{Bini96}{{15}{}{{}}{{}}}
\bibcite{Ostrowski41}{{16}{}{{}}{{}}}
\bibcite{Karimall98}{{17}{}{{}}{{}}}
\bibcite{Mirankar68}{{18}{}{{}}{{}}}
\bibcite{Mirankar71}{{19}{}{{}}{{}}}
\bibcite{Schedler72}{{20}{}{{}}{{}}}
\bibcite{Winogard72}{{21}{}{{}}{{}}}
\bibcite{Benall68}{{22}{}{{}}{{}}}
\bibcite{Jana06}{{23}{}{{}}{{}}}
\bibcite{Janall99}{{24}{}{{}}{{}}}
\bibcite{Riceall06}{{25}{}{{}}{{}}}
\bibcite{Azad07}{{26}{}{{}}{{}}}
\bibcite{Gemignani07}{{27}{}{{}}{{}}}
\bibcite{Kalantari08}{{28}{}{{}}{{}}}
\bibcite{Skachek08}{{29}{}{{}}{{}}}
\bibcite{Zhancall08}{{30}{}{{}}{{}}}
\bibcite{Zhuall08}{{31}{}{{}}{{}}}
\bibcite{Bini04}{{32}{}{{}}{{}}}
\bibcite{Cosnard90}{{33}{}{{}}{{}}}
\bibcite{Jana99}{{34}{}{{}}{{}}}
\bibcite{NVIDIA10}{{35}{}{{}}{{}}}
\providecommand\NAT@force@numbers{}\NAT@force@numbers