X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/blobdiff_plain/a601f08e009efccb69bc30f54a76342afca25273..26140afc30d94e735cf20b19eede8c4a697563ee:/elsarticle-template.aux

diff --git a/elsarticle-template.aux b/elsarticle-template.aux
index 751cc5f..29967a3 100644
--- a/elsarticle-template.aux
+++ b/elsarticle-template.aux
@@ -1,128 +1,128 @@
-\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*\HyPL@Entry[1]{}
-\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}}
-\HyPL@Entry{0<</S/D>>}
-\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}{}{{}}{{}}}
-\bibcite{Durand60}{{4}{}{{}}{{}}}
-\@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{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
+\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