]> AND Private Git Repository - kahina_paper1.git/blobdiff - elsarticle-template.aux
Logo AND Algorithmique Numérique Distribuée

Private GIT Repository
ajout fichier manquant
[kahina_paper1.git] / elsarticle-template.aux
index 751cc5f31272cb837430df6d744cea7090b107fe..29967a3bf577732ff0c08813fd57b8c112680a26 100644 (file)
-\relax \r
-\providecommand\hyper@newdestlabel[2]{}\r
-\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}\r
-\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined\r
-\global\let\oldcontentsline\contentsline\r
-\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}\r
-\global\let\oldnewlabel\newlabel\r
-\gdef\newlabel#1#2{\newlabelxx{#1}#2}\r
-\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}\r
-\AtEndDocument{\ifx\hyper@anchor\@undefined\r
-\let\contentsline\oldcontentsline\r
-\let\newlabel\oldnewlabel\r
-\fi}\r
-\fi}\r
-\global\let\hyper@last\relax \r
-\gdef\HyperFirstAtBeginDocument#1{#1}\r
-\providecommand*\HyPL@Entry[1]{}\r
-\bibstyle{elsarticle-num}\r
-\emailauthor{kahina.ghidouche@gmail.com}{Ghidouche Kahina\corref {mycorrespondingauthor}}\r
-\emailauthor{raphael.couturier@univ-fcomte.fr}{Couturier Raphael\corref {mycorrespondingauthor}}\r
-\emailauthor{ar.sider@univ-bejaia.dz}{Abderrahmane Sider\corref {mycorrespondingauthor}}\r
-\HyPL@Entry{0<</S/D>>}\r
-\Newlabel{mycorrespondingauthor}{1}\r
-\Newlabel{myfootnote}{1}\r
-\Newlabel{mymainaddress}{a}\r
-\Newlabel{mysecondaryaddress}{b}\r
-\@writefile{toc}{\contentsline {section}{\numberline {1}Root finding problem}{1}{section.1}}\r
-\citation{Weierstrass03}\r
-\citation{Ilie50}\r
-\citation{Docev62}\r
-\citation{Durand60}\r
-\citation{Kerner66}\r
-\citation{Borch-Supan63}\r
-\citation{Ehrlich67}\r
-\citation{Aberth73}\r
-\citation{Loizon83}\r
-\citation{Freeman89}\r
-\citation{Loizon83}\r
-\citation{Freemanall90}\r
-\citation{Raphaelall01}\r
-\citation{CUDA10}\r
-\citation{Kahinall14}\r
-\@writefile{toc}{\contentsline {paragraph}{}{3}{section*.1}}\r
-\citation{Aberth73}\r
-\citation{Weierstrass03}\r
-\citation{Aberth73}\r
-\citation{Bini96}\r
-\citation{Ostrowski41}\r
-\@writefile{toc}{\contentsline {section}{\numberline {2}Aberth method}{4}{section.2}}\r
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Polynomials Initialization}{4}{subsection.2.1}}\r
-\citation{Karimall98}\r
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}Vector $Z^{(0)}$ Initialization}{5}{subsection.2.2}}\r
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Iterative Function $H_{i}$}{5}{subsection.2.3}}\r
-\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Convergence condition}{5}{subsection.2.4}}\r
-\@writefile{toc}{\contentsline {section}{\numberline {3}Amelioration of Aberth method }{5}{section.3}}\r
-\citation{Karimall98}\r
-\citation{Mirankar68,Mirankar71}\r
-\citation{Schedler72}\r
-\citation{Winogard72}\r
-\citation{Benall68,Jana06,Janall99,Riceall06}\r
-\citation{Azad07,Gemignani07,Kalantari08,Skachek08,Zhancall08,Zhuall08}\r
-\citation{Bini04}\r
-\citation{Cosnard90,Freeman89,Freemanall90,,Jana99,Janall99}\r
-\citation{Freemanall90}\r
-\citation{Mirankar71}\r
-\@writefile{toc}{\contentsline {section}{\numberline {4}The implementation of simultaneous methods in a parallel computer}{6}{section.4}}\r
-\citation{Kahinall14}\r
-\citation{NVIDIA10}\r
-\@writefile{toc}{\contentsline {section}{\numberline {5}A parallel implementation of Aberth method}{8}{section.5}}\r
-\@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Background on the GPU architecture}{8}{subsection.5.1}}\r
-\@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Background on the CUDA Programming Model}{9}{subsection.5.2}}\r
-\@writefile{toc}{\contentsline {subsection}{\numberline {5.3} The implementation of Aberth method on GPU}{10}{subsection.5.3}}\r
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.3.1}A sequential Aberth algorithm}{10}{subsubsection.5.3.1}}\r
-\@writefile{loa}{\contentsline {algocf}{\numberline {1}{\ignorespaces Algorithm to find root polynomial with Aberth method}}{10}{algocf.1}}\r
-\@writefile{toc}{\contentsline {paragraph}{The execution time}{11}{section*.2}}\r
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.3.2}Parallelize the steps on GPU }{12}{subsubsection.5.3.2}}\r
-\@writefile{loa}{\contentsline {algocf}{\numberline {2}{\ignorespaces Algorithm to find root polynomial with Aberth method}}{13}{algocf.2}}\r
-\@writefile{loa}{\contentsline {algocf}{\numberline {3}{\ignorespaces A global Algorithm for the iterative function}}{14}{algocf.3}}\r
-\@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Experimental study}{14}{subsection.5.4}}\r
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.4.1}Definition of the polynomial used}{14}{subsubsection.5.4.1}}\r
-\bibdata{mybibfile}\r
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.4.2}The study condition}{15}{subsubsection.5.4.2}}\r
-\@writefile{toc}{\contentsline {subsubsection}{\numberline {5.4.3}Comparative study}{15}{subsubsection.5.4.3}}\r
-\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces the convergence of Aberth algorithm}}{15}{table.1}}\r
-\newlabel{tab:theConvergenceOfAberthAlgorithm}{{1}{15}{the convergence of Aberth algorithm}{table.1}{}}\r
-\@writefile{toc}{\contentsline {paragraph}{Aberth algorithm on CPU and GPU}{15}{table.1}}\r
-\@writefile{toc}{\contentsline {paragraph}{The impact of the thread's number into the convergence of Aberth algorithm}{15}{table.2}}\r
-\bibcite{Weierstrass03}{{1}{}{{}}{{}}}\r
-\bibcite{Ilie50}{{2}{}{{}}{{}}}\r
-\bibcite{Docev62}{{3}{}{{}}{{}}}\r
-\bibcite{Durand60}{{4}{}{{}}{{}}}\r
-\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces The impact of the thread's number into the convergence of Aberth algorithm}}{16}{table.2}}\r
-\newlabel{tab:Theimpactofthethread'snumberintotheconvergenceofAberthalgorithm}{{2}{16}{The impact of the thread's number into the convergence of Aberth algorithm}{table.2}{}}\r
-\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces Aberth algorithm compare to Durand-Kerner algorithm}}{16}{table.3}}\r
-\newlabel{tab:AberthAlgorithCompareToDurandKernerAlgorithm}{{3}{16}{Aberth algorithm compare to Durand-Kerner algorithm}{table.3}{}}\r
-\@writefile{toc}{\contentsline {paragraph}{A comparative study between Aberth and Durand-kerner algorithm}{16}{table.3}}\r
-\bibcite{Kerner66}{{5}{}{{}}{{}}}\r
-\bibcite{Borch-Supan63}{{6}{}{{}}{{}}}\r
-\bibcite{Ehrlich67}{{7}{}{{}}{{}}}\r
-\bibcite{Aberth73}{{8}{}{{}}{{}}}\r
-\bibcite{Loizon83}{{9}{}{{}}{{}}}\r
-\bibcite{Freeman89}{{10}{}{{}}{{}}}\r
-\bibcite{Freemanall90}{{11}{}{{}}{{}}}\r
-\bibcite{Raphaelall01}{{12}{}{{}}{{}}}\r
-\bibcite{CUDA10}{{13}{}{{}}{{}}}\r
-\bibcite{Kahinall14}{{14}{}{{}}{{}}}\r
-\bibcite{Bini96}{{15}{}{{}}{{}}}\r
-\bibcite{Ostrowski41}{{16}{}{{}}{{}}}\r
-\bibcite{Karimall98}{{17}{}{{}}{{}}}\r
-\bibcite{Mirankar68}{{18}{}{{}}{{}}}\r
-\bibcite{Mirankar71}{{19}{}{{}}{{}}}\r
-\bibcite{Schedler72}{{20}{}{{}}{{}}}\r
-\bibcite{Winogard72}{{21}{}{{}}{{}}}\r
-\bibcite{Benall68}{{22}{}{{}}{{}}}\r
-\bibcite{Jana06}{{23}{}{{}}{{}}}\r
-\bibcite{Janall99}{{24}{}{{}}{{}}}\r
-\bibcite{Riceall06}{{25}{}{{}}{{}}}\r
-\bibcite{Azad07}{{26}{}{{}}{{}}}\r
-\bibcite{Gemignani07}{{27}{}{{}}{{}}}\r
-\bibcite{Kalantari08}{{28}{}{{}}{{}}}\r
-\bibcite{Skachek08}{{29}{}{{}}{{}}}\r
-\bibcite{Zhancall08}{{30}{}{{}}{{}}}\r
-\bibcite{Zhuall08}{{31}{}{{}}{{}}}\r
-\bibcite{Bini04}{{32}{}{{}}{{}}}\r
-\bibcite{Cosnard90}{{33}{}{{}}{{}}}\r
-\bibcite{Jana99}{{34}{}{{}}{{}}}\r
-\bibcite{NVIDIA10}{{35}{}{{}}{{}}}\r
-\providecommand\NAT@force@numbers{}\NAT@force@numbers\r
+\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