From 05d52395f48a55ff95c2e917eaa90adfabc69d82 Mon Sep 17 00:00:00 2001
From: couturie <raphael.couturier@univ-fcomte.Fr>
Date: Tue, 20 Oct 2015 12:06:07 +0200
Subject: [PATCH] ajout fichier manquant

---
 Root.pdf                |  Bin 153495 -> 239201 bytes
 elsarticle-template.aux |  256 ++++-----
 elsarticle-template.bbl |  322 +++++------
 elsarticle-template.blg |   83 ++-
 elsarticle-template.log | 1123 +++++++++++++++++++++------------------
 elsarticle-template.out |   36 +-
 elsarticle-template.pdf |  Bin 103288 -> 297055 bytes
 elsarticle.cls          |  810 ++++++++++++++++++++++++++++
 8 files changed, 1786 insertions(+), 844 deletions(-)
 create mode 100644 elsarticle.cls

diff --git a/Root.pdf b/Root.pdf
index df62371f7f3bbafb8caee5f281bfa837988bd51a..0ee3f516ad3cb808a96bdf97ed6b37fd9e35ad2c 100644
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+\citation{Freeman89}
+\citation{Loizon83}
+\citation{Freemanall90}
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+\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}
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+\citation{Mirankar71}
+\@writefile{toc}{\contentsline {section}{\numberline {4}The implementation of simultaneous methods in a parallel computer}{6}{section.4}}
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+\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}}
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+\@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}}
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+\@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}}
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+\@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}{}{{}}{{}}}
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+\bibcite{Jana06}{{23}{}{{}}{{}}}
+\bibcite{Janall99}{{24}{}{{}}{{}}}
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+\bibcite{Kalantari08}{{28}{}{{}}{{}}}
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diff --git a/elsarticle-template.bbl b/elsarticle-template.bbl
index 606edd7..f884705 100644
--- a/elsarticle-template.bbl
+++ b/elsarticle-template.bbl
@@ -1,161 +1,161 @@
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-\expandafter\ifx\csname href\endcsname\relax
-  \def\href#1#2{#2} \def\path#1{#1}\fi
-
-\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}}.
-
-\bibitem{Docev62}
-K.~Docev, An alternative method of newton for simultaneous calculation of all
-  the roots of a given algebraic equation, Phys. Math. J~(5) (1962) 136--139.
-
-\bibitem{Durand60}
-E.~Durand, Solution numerique des equations algebriques, vol. 1, equations du
-  type f(x)=0, racines d'une polynome Vol.1.
-
-\bibitem{Kerner66}
-I.~Kerner, Ein gesamtschritteverfahren zur berechnung der nullstellen von
-  polynomen~(8) (1966) 290--294.
-
-\bibitem{Borch-Supan63}
-W.~Borch-Supan, A posteriori error for the zeros of polynomials~(5) (1963)
-  380--398.
-
-\bibitem{Ehrlich67}
-L.~Ehrlich, A modified newton method for polynomials, Comm. Ass. Comput.
-  Mach.~(10) (1967) 107--108.
-
-\bibitem{Aberth73}
-O.~Aberth, Iteration methods for finding all zeros of a polynomial
-  simultaneously, Mathematics of Computation 27~(122) (1973) 339--344.
-\newblock \href {http://dx.doi.org/10.1016/0003-4916(63)90068-X}
-  {\path{doi:10.1016/0003-4916(63)90068-X}}.
-
-\bibitem{Loizon83}
-G.~Loizon, Higher-order iteration functions for simultaneously approximating
-  polynomial zeros, Intern. J. Computer Math~(14) (1983) 45--58.
-
-\bibitem{Freeman89}
-T.~Freeman, Calculating polynomial zeros on a local memory parallel computer,
-  Parallel Computing~(12) (1989) 351--358.
-
-\bibitem{Freemanall90}
-T.~Freeman, R.~Brankin, Asynchronous polynomial zero-finding algorithms,
-  Parallel Computing~(17) (1990) 673--681.
-
-\bibitem{Raphaelall01}
-R.~Couturier, F.~Spetiri, Extraction de racines dans des polynômes creux de
-  degrées élevés.rsrcp (réseaux et systèmes répartis, calculateurs
-  parallèles), Algorithmes itératifs paralléles et distribués 1~(13) (1990)
-  67--81.
-
-\bibitem{CUDA10}
-Compute Unified Device Architecture Programming Guide Version 3.0.
-
-\bibitem{Kahinall14}
-K.~Ghidouche, R.~Couturie, A.~Sider, parallel implementation of the
-  durand-kerner algorithm for polynomial root-finding on gpu, IEEE. Conf. on
-  advanced Networking, Distributed Systems and Applications (2014) 53--57.
-
-\bibitem{Bini96}
-D.~Bini, Numerical computation of polynomial zeros by means of aberth s method,
-  Numerical Algorithms 13~(4) (1996) 179--200.
-
-\bibitem{Ostrowski41}
-A.~Ostrowski, On a theorem by j.l. walsh concerning the moduli of roots of
-  algebraic equations,bull. a.m.s., Algorithmes itératifs paralléles et
-  distribués 1~(47) (1941) 742--746.
-
-\bibitem{Karimall98}
-K.~Rhofir, F.~Spies, J.-C. Miellou, Perfectionnements de la méthode asynchrone
-  de durand-kerner pour les polynômes complexes, Calculateurs Parallèles
-  10~(4) (1998) 449--458.
-
-\bibitem{Mirankar68}
-W.~Mirankar, Parallel methods for approximating the roots of a function, IBM
-  Res Dev 30 (1968) 297--301.
-
-\bibitem{Mirankar71}
-W.~Mirankar, A survey of parallelism in numerical analysis, SIAM Rev (1971)
-  524--547.
-
-\bibitem{Schedler72}
-G.~Schedler, Parallel iteration methods in complexity of computer
-  communications, Commun ACM (1967) 286--290.
-
-\bibitem{Winogard72}
-S.~Winogard, Parallel iteration methods in complexity of computer
-  communications, Plenum, New York.
-
-\bibitem{Benall68}
-M.~Ben-Or, E.~Feig, D.~Kozzen, P.~Tiwary, A fast parallel algorithm for
-  determining all roots of a polynomial with real roots, Int: Proc of ACM
-  (1968) 340--349.
-
-\bibitem{Jana06}
-P.~Jana, Polynomial interpolation and polynomial root finding on otis-mesh,
-  Parallel Comput 32~(3) (2006) 301--312.
-
-\bibitem{Janall99}
-P.~Jana, B.~Sinha, R.~D. Gupta, Efficient parallel algorithms for finding
-  polynomial zeroes, Proc of the 6th int conference on advance computing, CDAC,
-  Pune University Campus,India 15~(3) (1999) 189--196.
-
-\bibitem{Riceall06}
-T.~Rice, L.~Jamieson, A highly parallel algorithm for root extraction, IEEE
-  Trans Comp 38~(3) (2006) 443--449.
-
-\bibitem{Azad07}
-H.~Azad, The performance of synchronous parallel polynomial root extraction on
-  a ring multicomputer, Clust Comput 2~(10) (2007) 167--174.
-
-\bibitem{Gemignani07}
-L.~Gemignani, Structured matrix methods for polynomial root finding., n: Proc
-  of the 2007 Intl symposium on symbolic and algebraic computation (2007)
-  175--180.
-
-\bibitem{Kalantari08}
-B.~Kalantari, Polynomial root finding and polynomiography., World
-  Scientifict,New Jersey.
-
-\bibitem{Skachek08}
-V.~Skachek, Structured matrix methods for polynomial root finding., n: Proc of
-  the 2007 Intl symposium on symbolic and algebraic computation (2008)
-  175--180.
-
-\bibitem{Zhancall08}
-X.~Zhanc, Z.~M.~Wan, A constrained learning algorithm for finding multiple real
-  roots of polynomial, In: Proc of the 2008 intl symposium on computational
-  intelligence and design (2008) 38--41.
-
-\bibitem{Zhuall08}
-W.~Zhu, w.~Zeng, D.~Lin, an adaptive algorithm finding multiple roots of
-  polynomials, Lect Notes Comput Sci~(5262) (2008) 674--681.
-
-\bibitem{Bini04}
-D.~Bini, L.~Gemignani, Inverse power and durand kerner iterations for
-  univariate polynomial root finding, Comput Math Appl~(47) (2004) 447--459.
-
-\bibitem{Cosnard90}
-M.~Cosnard, P.~Fraigniaud, Finding the roots of a polynomial on an mimd
-  multicomputer, Parallel Comput 15~(3) (1990) 75--85.
-
-\bibitem{Jana99}
-P.~Jana, Finding polynomial zeroes on a multi-mesh of trees (mmt), In: Proc of
-  the 2nd int conference on information technology (1999) 202--206.
-
-\bibitem{NVIDIA10}
-NVIDIA, NVIDIA CUDA C Programming Guide, Vol.~7 of 001, PG, 2015.
-
-\end{thebibliography}
+\begin{thebibliography}{10}
+\expandafter\ifx\csname url\endcsname\relax
+  \def\url#1{\texttt{#1}}\fi
+\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi
+\expandafter\ifx\csname href\endcsname\relax
+  \def\href#1#2{#2} \def\path#1{#1}\fi
+
+\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}}.
+
+\bibitem{Docev62}
+K.~Docev, An alternative method of newton for simultaneous calculation of all
+  the roots of a given algebraic equation, Phys. Math. J~(5) (1962) 136--139.
+
+\bibitem{Durand60}
+E.~Durand, Solution numerique des equations algebriques, vol. 1, equations du
+  type f(x)=0, racines d'une polynome Vol.1.
+
+\bibitem{Kerner66}
+I.~Kerner, Ein gesamtschritteverfahren zur berechnung der nullstellen von
+  polynomen~(8) (1966) 290--294.
+
+\bibitem{Borch-Supan63}
+W.~Borch-Supan, A posteriori error for the zeros of polynomials~(5) (1963)
+  380--398.
+
+\bibitem{Ehrlich67}
+L.~Ehrlich, A modified newton method for polynomials, Comm. Ass. Comput.
+  Mach.~(10) (1967) 107--108.
+
+\bibitem{Aberth73}
+O.~Aberth, Iteration methods for finding all zeros of a polynomial
+  simultaneously, Mathematics of Computation 27~(122) (1973) 339--344.
+\newblock \href {http://dx.doi.org/10.1016/0003-4916(63)90068-X}
+  {\path{doi:10.1016/0003-4916(63)90068-X}}.
+
+\bibitem{Loizon83}
+G.~Loizon, Higher-order iteration functions for simultaneously approximating
+  polynomial zeros, Intern. J. Computer Math~(14) (1983) 45--58.
+
+\bibitem{Freeman89}
+T.~Freeman, Calculating polynomial zeros on a local memory parallel computer,
+  Parallel Computing~(12) (1989) 351--358.
+
+\bibitem{Freemanall90}
+T.~Freeman, R.~Brankin, Asynchronous polynomial zero-finding algorithms,
+  Parallel Computing~(17) (1990) 673--681.
+
+\bibitem{Raphaelall01}
+R.~Couturier, F.~Spetiri, Extraction de racines dans des polynômes creux de
+  degrées élevés.rsrcp (réseaux et systèmes répartis, calculateurs
+  parallèles), Algorithmes itératifs paralléles et distribués 1~(13) (1990)
+  67--81.
+
+\bibitem{CUDA10}
+Compute Unified Device Architecture Programming Guide Version 3.0.
+
+\bibitem{Kahinall14}
+K.~Ghidouche, R.~Couturie, A.~Sider, parallel implementation of the
+  durand-kerner algorithm for polynomial root-finding on gpu, IEEE. Conf. on
+  advanced Networking, Distributed Systems and Applications (2014) 53--57.
+
+\bibitem{Bini96}
+D.~Bini, Numerical computation of polynomial zeros by means of aberth s method,
+  Numerical Algorithms 13~(4) (1996) 179--200.
+
+\bibitem{Ostrowski41}
+A.~Ostrowski, On a theorem by j.l. walsh concerning the moduli of roots of
+  algebraic equations,bull. a.m.s., Algorithmes itératifs paralléles et
+  distribués 1~(47) (1941) 742--746.
+
+\bibitem{Karimall98}
+K.~Rhofir, F.~Spies, J.-C. Miellou, Perfectionnements de la méthode asynchrone
+  de durand-kerner pour les polynômes complexes, Calculateurs Parallèles
+  10~(4) (1998) 449--458.
+
+\bibitem{Mirankar68}
+W.~Mirankar, Parallel methods for approximating the roots of a function, IBM
+  Res Dev 30 (1968) 297--301.
+
+\bibitem{Mirankar71}
+W.~Mirankar, A survey of parallelism in numerical analysis, SIAM Rev (1971)
+  524--547.
+
+\bibitem{Schedler72}
+G.~Schedler, Parallel iteration methods in complexity of computer
+  communications, Commun ACM (1967) 286--290.
+
+\bibitem{Winogard72}
+S.~Winogard, Parallel iteration methods in complexity of computer
+  communications, Plenum, New York.
+
+\bibitem{Benall68}
+M.~Ben-Or, E.~Feig, D.~Kozzen, P.~Tiwary, A fast parallel algorithm for
+  determining all roots of a polynomial with real roots, Int: Proc of ACM
+  (1968) 340--349.
+
+\bibitem{Jana06}
+P.~Jana, Polynomial interpolation and polynomial root finding on otis-mesh,
+  Parallel Comput 32~(3) (2006) 301--312.
+
+\bibitem{Janall99}
+P.~Jana, B.~Sinha, R.~D. Gupta, Efficient parallel algorithms for finding
+  polynomial zeroes, Proc of the 6th int conference on advance computing, CDAC,
+  Pune University Campus,India 15~(3) (1999) 189--196.
+
+\bibitem{Riceall06}
+T.~Rice, L.~Jamieson, A highly parallel algorithm for root extraction, IEEE
+  Trans Comp 38~(3) (2006) 443--449.
+
+\bibitem{Azad07}
+H.~Azad, The performance of synchronous parallel polynomial root extraction on
+  a ring multicomputer, Clust Comput 2~(10) (2007) 167--174.
+
+\bibitem{Gemignani07}
+L.~Gemignani, Structured matrix methods for polynomial root finding., n: Proc
+  of the 2007 Intl symposium on symbolic and algebraic computation (2007)
+  175--180.
+
+\bibitem{Kalantari08}
+B.~Kalantari, Polynomial root finding and polynomiography., World
+  Scientifict,New Jersey.
+
+\bibitem{Skachek08}
+V.~Skachek, Structured matrix methods for polynomial root finding., n: Proc of
+  the 2007 Intl symposium on symbolic and algebraic computation (2008)
+  175--180.
+
+\bibitem{Zhancall08}
+X.~Zhanc, Z.~M.~Wan, A constrained learning algorithm for finding multiple real
+  roots of polynomial, In: Proc of the 2008 intl symposium on computational
+  intelligence and design (2008) 38--41.
+
+\bibitem{Zhuall08}
+W.~Zhu, w.~Zeng, D.~Lin, an adaptive algorithm finding multiple roots of
+  polynomials, Lect Notes Comput Sci~(5262) (2008) 674--681.
+
+\bibitem{Bini04}
+D.~Bini, L.~Gemignani, Inverse power and durand kerner iterations for
+  univariate polynomial root finding, Comput Math Appl~(47) (2004) 447--459.
+
+\bibitem{Cosnard90}
+M.~Cosnard, P.~Fraigniaud, Finding the roots of a polynomial on an mimd
+  multicomputer, Parallel Comput 15~(3) (1990) 75--85.
+
+\bibitem{Jana99}
+P.~Jana, Finding polynomial zeroes on a multi-mesh of trees (mmt), In: Proc of
+  the 2nd int conference on information technology (1999) 202--206.
+
+\bibitem{NVIDIA10}
+NVIDIA, NVIDIA CUDA C Programming Guide, Vol.~7 of 001, PG, 2015.
+
+\end{thebibliography}
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diff --git a/elsarticle-template.log b/elsarticle-template.log
index 8fd7379..1b0f73e 100644
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diff --git a/elsarticle-template.out b/elsarticle-template.out
index 202aedb..1f64cfb 100644
--- a/elsarticle-template.out
+++ b/elsarticle-template.out
@@ -1,18 +1,18 @@
-\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
+\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
diff --git a/elsarticle-template.pdf b/elsarticle-template.pdf
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diff --git a/elsarticle.cls b/elsarticle.cls
new file mode 100644
index 0000000..1b15bce
--- /dev/null
+++ b/elsarticle.cls
@@ -0,0 +1,810 @@
+%%
+%% This is file `elsarticle.cls',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% elsarticle.dtx  (with options: `class')
+%% 
+%% Copyright 2007, 2008, 2009 Elsevier Ltd
+%% 
+%% This file is part of the 'Elsarticle Bundle'.
+%% -------------------------------------------
+%% 
+%% It may be distributed under the conditions of the LaTeX Project Public
+%% License, either version 1.2 of this license or (at your option) any
+%% later version.  The latest version of this license is in
+%%    http://www.latex-project.org/lppl.txt
+%% and version 1.2 or later is part of all distributions of LaTeX
+%% version 1999/12/01 or later.
+%% 
+%% The list of all files belonging to the 'Elsarticle Bundle' is
+%% given in the file `manifest.txt'.
+%% 
+%%
+%% $Id: elsarticle.dtx 19 2009-12-17 07:07:52Z rishi $
+%%
+ \def\RCSfile{elsarticle}%
+ \def\RCSversion{1.20b}%
+ \def\RCSdate{2009/09/17}%
+ \def\@shortjnl{\relax}
+ \def\@journal{Elsevier Ltd} \def\@company{Elsevier Ltd}
+ \def\@issn{000-0000}
+ \def\@shortjid{elsarticle}
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+\ProvidesClass{\@shortjid}[\RCSdate, \RCSversion: \@journal]
+\def\ABD{\AtBeginDocument}
+\newif\ifpreprint \preprintfalse
+\newif\iflongmktitle \longmktitlefalse
+
+\def\@blstr{1}
+\newdimen\@bls
+\@bls=\baselineskip
+
+\def\@finalWarning{%
+  *****************************************************\MessageBreak
+   This document is typeset in the CRC style which\MessageBreak
+   is not suitable for submission.\MessageBreak
+   \MessageBreak
+   Please typeset again using 'preprint' option\MessageBreak
+   for creating PDF suitable for submission.\MessageBreak
+  ******************************************************\MessageBreak
+}
+
+\DeclareOption{preprint}{\global\preprinttrue
+  \gdef\@blstr{1}\xdef\jtype{0}%
+   \AtBeginDocument{\@twosidefalse\@mparswitchfalse}}
+\DeclareOption{final}{\gdef\@blstr{1}\global\preprintfalse}
+\DeclareOption{review}{\global\preprinttrue\gdef\@blstr{1.5}}
+\DeclareOption{authoryear}{\xdef\@biboptions{round,authoryear}}
+\DeclareOption{number}{\xdef\@biboptions{numbers}}
+\DeclareOption{numbers}{\xdef\@biboptions{numbers}}
+\DeclareOption{longtitle}{\global\longmktitletrue}
+\DeclareOption{5p}{\xdef\jtype{5}\global\preprintfalse
+  \ExecuteOptions{twocolumn}}
+  \def\jtype{0}
+\DeclareOption{3p}{\xdef\jtype{3}\global\preprintfalse}
+\DeclareOption{1p}{\xdef\jtype{1}\global\preprintfalse
+  \AtBeginDocument{\@twocolumnfalse}}
+\DeclareOption{times}{\IfFileExists{txfonts.sty}%
+  {\AtEndOfClass{\RequirePackage{txfonts}%
+  \gdef\ttdefault{cmtt}%
+   \let\iint\relax
+  \let\iiint\relax
+  \let\iiiint\relax
+  \let\idotsint\relax
+  \let\openbox\relax}}{\RequirePackage{times}}}
+\ExecuteOptions{a4paper,10pt,oneside,onecolumn,number,preprint}
+\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}}
+\ProcessOptions
+\LoadClass{article}
+\RequirePackage{graphicx}
+\let\comma\@empty
+\let\tnotesep\@empty
+\def\title#1{\gdef\@title{#1}}
+\let\@title\@empty
+
+\def\elsLabel#1{\@bsphack\protected@write\@auxout{}%
+         {\string\Newlabel{#1}{\@currentlabel}}\@esphack}
+\def\Newlabel#1#2{\expandafter\xdef\csname X@#1\endcsname{#2}}
+
+\def\elsRef#1{\@ifundefined{X@#1}{0}{\csname X@#1\endcsname}%
+}
+
+\def\tnotemark[#1]{\textsuperscript{\@for\@@tmark:=#1\do{%
+      \edef\tnotenum{\@ifundefined{X@\@@tmark}{1}{\elsRef{\@@tmark}}}%
+      \ifcase\tnotenum\or\ding{73}\or,\ding{73}\ding{73}\fi}}%
+}
+\let\@tnotemark\@empty
+
+\let\@tnotes\@empty
+\RequirePackage{pifont}
+\newcounter{tnote}
+\def\tnotetext[#1]#2{\g@addto@macro\@tnotes{%
+  \refstepcounter{tnote}\elsLabel{#1}%
+   \def\thefootnote{\ifcase\c@tnote\or\ding{73}\or\ding{73}\ding{73}\fi}%
+    \footnotetext{#2}}}
+
+\let\@nonumnotes\@empty
+\def\nonumnote#1{\g@addto@macro\@nonumnotes{%
+     \let\thefootnote\relax\footnotetext{#1}}}
+
+\newcounter{fnote}
+\def\fnmark[#1]{\let\comma\@empty
+    \def\@fnmark{\@for\@@fnmark:=#1\do{%
+    \edef\fnotenum{\@ifundefined{X@\@@fnmark}{1}{\elsRef{\@@fnmark}}}%
+  \unskip\comma\fnotenum\let\comma,}}%
+}
+
+\let\@fnotes\@empty\let\@fnmark\@empty
+\def\fntext[#1]#2{\g@addto@macro\@fnotes{%
+     \refstepcounter{fnote}\elsLabel{#1}%
+   \def\thefootnote{\thefnote}%
+   \global\setcounter{footnote}{\thefnote}%
+   \footnotetext{#2}}}
+
+\def\cormark[#1]{\edef\cnotenum{\elsRef{#1}}%
+    \unskip\textsuperscript{\sep\ifcase\cnotenum\or
+       $\ast$\or$\ast\ast$\fi\hspace{-1pt}}\let\sep=,}
+
+\let\@cormark\@empty
+\let\@cornotes\@empty
+\newcounter{cnote}
+\def\cortext[#1]#2{\g@addto@macro\@cornotes{%
+    \refstepcounter{cnote}\elsLabel{#1}%
+    \def\thefootnote{\ifcase\thecnote\or$\ast$\or
+    $\ast\ast$\fi}%
+    \footnotetext{#2}}}
+
+\let\@corref\@empty
+\def\corref#1{\edef\cnotenum{\elsRef{#1}}%
+    \edef\@corref{\ifcase\cnotenum\or
+         $\ast$\or$\ast\ast$\fi\hskip-1pt}}
+
+\def\fnref#1{\fnmark[#1]}
+\def\tnoteref#1{\tnotemark[#1]}
+
+\def\resetTitleCounters{\c@cnote=0
+   \c@fnote=0 \c@tnote=0 \c@footnote=0}
+
+\let\eadsep\@empty
+\let\@elseads\@empty
+\let\@elsuads\@empty
+\let\@cormark\@empty
+\def\hashchar{\expandafter\@gobble\string\~}
+\def\underscorechar{\expandafter\@gobble\string\_}
+\def\lbracechar{\expandafter\@gobble\string\{}
+\def\rbracechar{\expandafter\@gobble\string\}}
+
+\def\ead{\@ifnextchar[{\@uad}{\@ead}}
+\gdef\@ead#1{\bgroup\def\_{\string\underscorechar\space}%
+  \def\{{\string\lbracechar\space}%
+   \def~{\hashchar\space}%
+   \def\}{\string\rbracechar\space}%
+   \edef\tmp{\the\@eadauthor}
+   \immediate\write\@auxout{\string\emailauthor
+     {#1}{\expandafter\strip@prefix\meaning\tmp}}%
+  \egroup
+}
+\newcounter{ead}
+\gdef\emailauthor#1#2{\stepcounter{ead}%
+     \g@addto@macro\@elseads{\raggedright%
+      \let\corref\@gobble
+      \eadsep\texttt{#1} (#2)\def\eadsep{\unskip,\space}}%
+}
+\gdef\@uad[#1]#2{\bgroup
+  \def~{\string\hashchar\space}%
+  \def\_{\string\underscorechar\space}%
+   \edef\tmp{\the\@eadauthor}
+   \immediate\write\@auxout{\string\urlauthor
+     {#2}{\expandafter\strip@prefix\meaning\tmp}}%
+  \egroup
+}
+\def\urlauthor#1#2{\g@addto@macro\@elsuads{\let\corref\@gobble%
+     \raggedright\eadsep\texttt{#1}\space(#2)%
+     \def\eadsep{\unskip,\space}}%
+}
+
+\def\elsauthors{}
+\def\pprinttitle{}
+\let\authorsep\@empty
+\let\sep\@empty
+\newcounter{author}
+\def\author{\@ifnextchar[{\@@author}{\@author}}
+
+\newtoks\@eadauthor
+\def\@@author[#1]#2{\g@addto@macro\elsauthors{%
+    \def\baselinestretch{1}%
+    \authorsep#2\unskip\textsuperscript{%#1%
+      \@for\@@affmark:=#1\do{%
+       \edef\affnum{\@ifundefined{X@\@@affmark}{1}{\elsRef{\@@affmark}}}%
+     \unskip\sep\affnum\let\sep=,}%
+      \ifx\@fnmark\@empty\else\unskip\sep\@fnmark\let\sep=,\fi
+      \ifx\@corref\@empty\else\unskip\sep\@corref\let\sep=,\fi
+      }%
+    \def\authorsep{\unskip,\space}%
+    \global\let\sep\@empty\global\let\@corref\@empty
+    \global\let\@fnmark\@empty}%
+    \@eadauthor={#2}
+}
+
+\def\@author#1{\g@addto@macro\elsauthors{\normalsize%
+    \def\baselinestretch{1}%
+    \upshape\authorsep#1\unskip\textsuperscript{%
+      \ifx\@fnmark\@empty\else\unskip\sep\@fnmark\let\sep=,\fi
+      \ifx\@corref\@empty\else\unskip\sep\@corref\let\sep=,\fi
+      }%
+    \def\authorsep{\unskip,\space}%
+    \global\let\@fnmark\@empty
+    \global\let\@corref\@empty
+    \global\let\sep\@empty}%
+    \@eadauthor={#1}
+}
+
+\def\elsaddress{}
+\def\addsep{\par\vskip6pt}
+\def\address{\@ifnextchar[{\@@address}{\@address}}
+
+\def\@alph#1{%
+  \ifcase#1\or a\or b\or c\or d\or e\or f\or g\or h\or i\or j\or k\or
+  l\or m\or n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or
+  y\or z%
+  \or aa\or ab\or ac\or ad\or ae\or af\or ag\or ah\or ai\or aj\or
+  ak\or al\or am\or an\or ao\or ap\or aq\or ar\or as\or at\or au\or
+  av\or aw\or ax\or ay\or az%
+  \or ba\or bb\or bc\or bd\or be\or bf\or bg\or bh\or bi\or bj\or
+  bk\or bl\or bm\or bn\or bo\or bp\or bq\or br\or bs\or bt\or bu\or
+  bv\or bw\or bx\or by\or bz%
+  \or ca\or cb\or cc\or cd\or ce\or cf\or cg\or ch\or ci\or cj\or
+  ck\or cl\or cm\or cn\or co\or cp\or cq\or cr\or cs\or ct\or cu\or
+  cv\or cw\or cx\or cy\or cz%
+  \or da\or db\or dc\or dd\or de\or df\or dg\or dh\or di\or dj\or
+  dk\or dl\or dm\or dn\or do\or dp\or dq\or dr\or ds\or dt\or du\or
+  dv\or dw\or dx\or dy\or dz%
+  \or ea\or eb\or ec\or ed\or ee\or ef\or eg\or eh\or ei\or ej\or
+  ek\or el\or em\or en\or eo\or ep\or eq\or er\or es\or et\or eu\or
+  ev\or ew\or ex\or ey\or ez%
+  \or fa\or fb\or fc\or fd\or fe\or ff\or fg\or fh\or fi\or fj\or
+  fk\or fl\or fm\or fn\or fo\or fp\or fq\or fr\or fs\or ft\or fu\or
+  fv\or fw\or fx\or fy\or fz%
+  \or ga\or gb\or gc\or gd\or ge\or gf\or gg\or gh\or gi\or gj\or
+  gk\or gl\or gm\or gn\or go\or gp\or gq\or gr\or gs\or gt\or gu\or
+  gv\or gw\or gx\or gy\or gz%
+  \else\@ctrerr\fi}
+
+\newcounter{affn}
+\renewcommand\theaffn{\alph{affn}}
+
+\long\def\@@address[#1]#2{\g@addto@macro\elsaddress{%
+    \def\baselinestretch{1}%
+     \refstepcounter{affn}
+     \xdef\@currentlabel{\theaffn}
+     \elsLabel{#1}%
+    \textsuperscript{\theaffn}#2\par}}
+
+\long\def\@address#1{\g@addto@macro\elsauthors{%
+    \def\baselinestretch{1}%
+    \addsep\footnotesize\itshape#1\def\addsep{\par\vskip6pt}%
+    \def\authorsep{\par\vskip8pt}}}
+
+\newbox\absbox
+\renewenvironment{abstract}{\global\setbox\absbox=\vbox\bgroup
+  \hsize=\textwidth\def\baselinestretch{1}%
+  \noindent\unskip\textbf{Abstract}
+ \par\medskip\noindent\unskip\ignorespaces}
+ {\egroup}
+
+\newbox\keybox
+\def\keyword{%
+  \def\sep{\unskip, }%
+ \def\MSC{\@ifnextchar[{\@MSC}{\@MSC[2000]}}
+  \def\@MSC[##1]{\par\leavevmode\hbox {\it ##1~MSC:\space}}%
+  \def\PACS{\par\leavevmode\hbox {\it PACS:\space}}%
+  \def\JEL{\par\leavevmode\hbox {\it JEL:\space}}%
+  \global\setbox\keybox=\vbox\bgroup\hsize=\textwidth
+  \normalsize\normalfont\def\baselinestretch{1}
+  \parskip\z@
+  \noindent\textit{Keywords: }
+  \raggedright                         % Keywords are not justified.
+  \ignorespaces}
+\def\endkeyword{\par \egroup}
+
+\newdimen\Columnwidth
+\Columnwidth=\columnwidth
+
+\def\printFirstPageNotes{%
+  \iflongmktitle
+   \let\columnwidth=\textwidth\fi
+  \ifx\@tnotes\@empty\else\@tnotes\fi
+  \ifx\@nonumnotes\@empty\else\@nonumnotes\fi
+  \ifx\@cornotes\@empty\else\@cornotes\fi
+  \ifx\@elseads\@empty\relax\else
+   \let\thefootnote\relax
+   \footnotetext{\ifnum\theead=1\relax
+      \textit{Email address:\space}\else
+      \textit{Email addresses:\space}\fi
+     \@elseads}\fi
+  \ifx\@elsuads\@empty\relax\else
+   \let\thefootnote\relax
+   \footnotetext{\textit{URL:\space}%
+     \@elsuads}\fi
+  \ifx\@fnotes\@empty\else\@fnotes\fi
+  \iflongmktitle\if@twocolumn
+   \let\columnwidth=\Columnwidth\fi\fi
+}
+
+\long\def\pprintMaketitle{\clearpage
+  \iflongmktitle\if@twocolumn\let\columnwidth=\textwidth\fi\fi
+  \resetTitleCounters
+  \def\baselinestretch{1}%
+  \printFirstPageNotes
+  \begin{center}%
+ \thispagestyle{pprintTitle}%
+   \def\baselinestretch{1}%
+    \Large\@title\par\vskip18pt
+    \normalsize\elsauthors\par\vskip10pt
+    \footnotesize\itshape\elsaddress\par\vskip36pt
+    \hrule\vskip12pt
+    \ifvoid\absbox\else\unvbox\absbox\par\vskip10pt\fi
+    \ifvoid\keybox\else\unvbox\keybox\par\vskip10pt\fi
+    \hrule\vskip12pt
+    \end{center}%
+  \gdef\thefootnote{\arabic{footnote}}%
+  }
+
+\def\printWarning{%
+     \mbox{}\par\vfill\par\bgroup
+     \fboxsep12pt\fboxrule1pt
+     \hspace*{.18\textwidth}
+     \fcolorbox{gray50}{gray10}{\box\warnbox}
+     \egroup\par\vfill\thispagestyle{empty}
+     \setcounter{page}{0}
+     \clearpage}
+
+\long\def\finalMaketitle{%
+  \resetTitleCounters
+  \def\baselinestretch{1}%
+   \MaketitleBox
+   \thispagestyle{pprintTitle}%
+  \gdef\thefootnote{\arabic{footnote}}%
+  }
+
+\long\def\MaketitleBox{%
+  \resetTitleCounters
+  \def\baselinestretch{1}%
+  \begin{center}%
+   \def\baselinestretch{1}%
+    \Large\@title\par\vskip18pt
+    \normalsize\elsauthors\par\vskip10pt
+    \footnotesize\itshape\elsaddress\par\vskip36pt
+    \hrule\vskip12pt
+    \ifvoid\absbox\else\unvbox\absbox\par\vskip10pt\fi
+    \ifvoid\keybox\else\unvbox\keybox\par\vskip10pt\fi
+    \hrule\vskip12pt
+    \end{center}%
+  }
+
+\def\FNtext#1{\par\bgroup\footnotesize#1\egroup}
+\newdimen\space@left
+\def\alarm#1{\typeout{******************************}%
+             \typeout{#1}%
+             \typeout{******************************}%
+}
+\long\def\getSpaceLeft{%\global\@twocolumnfalse%
+   \global\setbox0=\vbox{\hsize=\textwidth\MaketitleBox}%
+   \global\setbox1=\vbox{\hsize=\textwidth
+    \let\footnotetext\FNtext
+    \printFirstPageNotes}%
+    \xdef\noteheight{\the\ht1}%
+    \xdef\titleheight{\the\ht0}%
+    \@tempdima=\vsize
+    \advance\@tempdima-\noteheight
+    \advance\@tempdima-1\baselineskip
+}
+
+  \skip\footins=24pt
+
+\newbox\els@boxa
+\newbox\els@boxb
+
+\ifpreprint
+  \def\maketitle{\pprintMaketitle}
+  \else
+   \ifnum\jtype=1
+    \def\maketitle{%
+      \iflongmktitle\getSpaceLeft
+       \global\setbox\els@boxa=\vsplit0 to \@tempdima
+       \box\els@boxa\par\resetTitleCounters
+       \thispagestyle{pprintTitle}%
+       \printFirstPageNotes
+       \box0%
+      \else
+       \finalMaketitle\printFirstPageNotes
+      \fi
+    \gdef\thefootnote{\arabic{footnote}}}%
+  \else
+ \ifnum\jtype=5
+    \def\maketitle{%
+      \iflongmktitle\getSpaceLeft
+       \global\setbox\els@boxa=\vsplit0 to \@tempdima
+       \box\els@boxa\par\resetTitleCounters
+       \thispagestyle{pprintTitle}%
+       \printFirstPageNotes
+       \twocolumn[\box0]%\printFirstPageNotes
+      \else
+       \twocolumn[\finalMaketitle]\printFirstPageNotes
+     \fi
+     \gdef\thefootnote{\arabic{footnote}}}
+  \else
+  \if@twocolumn
+    \def\maketitle{%
+      \iflongmktitle\getSpaceLeft
+       \global\setbox\els@boxa=\vsplit0 to \@tempdima
+       \box\els@boxa\par\resetTitleCounters
+       \thispagestyle{pprintTitle}%
+       \printFirstPageNotes
+       \twocolumn[\box0]%
+      \else
+       \twocolumn[\finalMaketitle]\printFirstPageNotes
+      \fi
+     \gdef\thefootnote{\arabic{footnote}}}%
+   \else
+    \def\maketitle{%
+      \iflongmktitle\getSpaceLeft
+       \global\setbox\els@boxa=\vsplit0 to \@tempdima
+       \box\els@boxa\par\resetTitleCounters
+       \thispagestyle{pprintTitle}%
+       \printFirstPageNotes
+       \box0%
+     \else
+       \finalMaketitle\printFirstPageNotes
+      \fi
+    \gdef\thefootnote{\arabic{footnote}}}%
+   \fi
+  \fi
+ \fi
+\fi
+\def\ps@pprintTitle{%
+     \let\@oddhead\@empty
+     \let\@evenhead\@empty
+     \def\@oddfoot{\footnotesize\itshape
+       Preprint submitted to \ifx\@journal\@empty Elsevier
+       \else\@journal\fi\hfill\today}%
+     \let\@evenfoot\@oddfoot}
+\def\@seccntDot{.}
+\def\@seccntformat#1{\csname the#1\endcsname\@seccntDot\hskip 0.5em}
+
+\renewcommand\section{\@startsection {section}{1}{\z@}%
+           {18\p@ \@plus 6\p@ \@minus 3\p@}%
+           {9\p@ \@plus 6\p@ \@minus 3\p@}%
+           {\normalsize\bfseries\boldmath}}
+\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%
+           {12\p@ \@plus 6\p@ \@minus 3\p@}%
+           {3\p@ \@plus 6\p@ \@minus 3\p@}%
+           {\normalfont\normalsize\itshape}}
+\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%
+           {12\p@ \@plus 6\p@ \@minus 3\p@}%
+           {\p@}%
+           {\normalfont\normalsize\itshape}}
+
+\def\paragraph{\secdef{\els@aparagraph}{\els@bparagraph}}
+\def\els@aparagraph[#1]#2{\elsparagraph[#1]{#2.}}
+\def\els@bparagraph#1{\elsparagraph*{#1.}}
+
+\newcommand\elsparagraph{\@startsection{paragraph}{4}{0\z@}%
+           {10\p@ \@plus 6\p@ \@minus 3\p@}%
+           {-6\p@}%
+           {\normalfont\itshape}}
+\newdimen\leftMargin
+\leftMargin=2em
+\newtoks\@enLab  %\newtoks\@enfont
+\def\@enQmark{?}
+\def\@enLabel#1#2{%
+  \edef\@enThe{\noexpand#1{\@enumctr}}%
+  \@enLab\expandafter{\the\@enLab\csname the\@enumctr\endcsname}%
+  \@enloop}
+\def\@enSpace{\afterassignment\@enSp@ce\let\@tempa= }
+\def\@enSp@ce{\@enLab\expandafter{\the\@enLab\space}\@enloop}
+\def\@enGroup#1{\@enLab\expandafter{\the\@enLab{#1}}\@enloop}
+\def\@enOther#1{\@enLab\expandafter{\the\@enLab#1}\@enloop}
+\def\@enloop{\futurelet\@entemp\@enloop@}
+\def\@enloop@{%
+  \ifx A\@entemp         \def\@tempa{\@enLabel\Alph  }\else
+  \ifx a\@entemp         \def\@tempa{\@enLabel\alph  }\else
+  \ifx i\@entemp         \def\@tempa{\@enLabel\roman }\else
+  \ifx I\@entemp         \def\@tempa{\@enLabel\Roman }\else
+  \ifx 1\@entemp         \def\@tempa{\@enLabel\arabic}\else
+  \ifx \@sptoken\@entemp \let\@tempa\@enSpace         \else
+  \ifx \bgroup\@entemp   \let\@tempa\@enGroup         \else
+  \ifx \@enum@\@entemp   \let\@tempa\@gobble          \else
+                         \let\@tempa\@enOther
+             \fi\fi\fi\fi\fi\fi\fi\fi
+  \@tempa}
+\newlength{\@sep} \newlength{\@@sep}
+\setlength{\@sep}{.5\baselineskip plus.2\baselineskip
+            minus.2\baselineskip}
+\setlength{\@@sep}{.1\baselineskip plus.01\baselineskip
+            minus.05\baselineskip}
+\providecommand{\sfbc}{\rmfamily\upshape}
+\providecommand{\sfn}{\rmfamily\upshape}
+\def\@enfont{\ifnum \@enumdepth >1\let\@nxt\sfn \else\let\@nxt\sfbc \fi\@nxt}
+\def\enumerate{%
+   \ifnum \@enumdepth >3 \@toodeep\else
+      \advance\@enumdepth \@ne
+      \edef\@enumctr{enum\romannumeral\the\@enumdepth}\fi
+   \@ifnextchar[{\@@enum@}{\@enum@}}
+\def\@@enum@[#1]{%
+  \@enLab{}\let\@enThe\@enQmark
+  \@enloop#1\@enum@
+  \ifx\@enThe\@enQmark\@warning{The counter will not be printed.%
+   ^^J\space\@spaces\@spaces\@spaces The label is: \the\@enLab}\fi
+  \expandafter\edef\csname label\@enumctr\endcsname{\the\@enLab}%
+  \expandafter\let\csname the\@enumctr\endcsname\@enThe
+  \csname c@\@enumctr\endcsname7
+  \expandafter\settowidth
+            \csname leftmargin\romannumeral\@enumdepth\endcsname
+            {\the\@enLab\hskip\labelsep}%
+  \@enum@}
+\def\@enum@{\list{{\@enfont\csname label\@enumctr\endcsname}}%
+           {\usecounter{\@enumctr}\def\makelabel##1{\hss\llap{##1}}%
+     \ifnum \@enumdepth>1\setlength{\topsep}{\@@sep}\else
+           \setlength{\topsep}{\@sep}\fi
+     \ifnum \@enumdepth>1\setlength{\itemsep}{0pt plus1pt minus1pt}%
+      \else \setlength{\itemsep}{\@@sep}\fi
+     %\setlength\leftmargin{\leftMargin}%%%{1.8em}
+     \setlength{\parsep}{0pt plus1pt minus1pt}%
+     \setlength{\parskip}{0pt plus1pt minus1pt}
+                   }}
+
+\def\endenumerate{\par\ifnum \@enumdepth >1\addvspace{\@@sep}\else
+           \addvspace{\@sep}\fi \endlist}
+
+\def\sitem{\@noitemargtrue\@item[\@itemlabel *]}
+
+\def\itemize{\@ifnextchar[{\@Itemize}{\@Itemize[]}}
+
+\def\@Itemize[#1]{\def\next{#1}%
+  \ifnum \@itemdepth >\thr@@\@toodeep\else
+   \advance\@itemdepth\@ne
+  \ifx\next\@empty\else\expandafter\def\csname
+   labelitem\romannumeral\the\@itemdepth\endcsname{#1}\fi%
+  \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%
+  \expandafter\list\csname\@itemitem\endcsname
+  {\def\makelabel##1{\hss\llap{##1}}}%
+ \fi}
+\def\newdefinition#1{%
+  \@ifnextchar[{\@odfn{#1}}{\@ndfn{#1}}}%]
+\def\@ndfn#1#2{%
+  \@ifnextchar[{\@xndfn{#1}{#2}}{\@yndfn{#1}{#2}}}
+\def\@xndfn#1#2[#3]{%
+  \expandafter\@ifdefinable\csname #1\endcsname
+    {\@definecounter{#1}\@newctr{#1}[#3]%
+     \expandafter\xdef\csname the#1\endcsname{%
+       \expandafter\noexpand\csname the#3\endcsname \@dfncountersep
+          \@dfncounter{#1}}%
+     \global\@namedef{#1}{\@dfn{#1}{#2}}%
+     \global\@namedef{end#1}{\@enddefinition}}}
+\def\@yndfn#1#2{%
+  \expandafter\@ifdefinable\csname #1\endcsname
+    {\@definecounter{#1}%
+     \expandafter\xdef\csname the#1\endcsname{\@dfncounter{#1}}%
+     \global\@namedef{#1}{\@dfn{#1}{#2}}%
+     \global\@namedef{end#1}{\@enddefinition}}}
+\def\@odfn#1[#2]#3{%
+  \@ifundefined{c@#2}{\@nocounterr{#2}}%
+    {\expandafter\@ifdefinable\csname #1\endcsname
+    {\global\@namedef{the#1}{\@nameuse{the#2}}
+  \global\@namedef{#1}{\@dfn{#2}{#3}}%
+  \global\@namedef{end#1}{\@enddefinition}}}}
+\def\@dfn#1#2{%
+  \refstepcounter{#1}%
+  \@ifnextchar[{\@ydfn{#1}{#2}}{\@xdfn{#1}{#2}}}
+\def\@xdfn#1#2{%
+  \@begindefinition{#2}{\csname the#1\endcsname}\ignorespaces}
+\def\@ydfn#1#2[#3]{%
+  \@opargbegindefinition{#2}{\csname the#1\endcsname}{#3}\ignorespaces}
+\def\@dfncounter#1{\noexpand\arabic{#1}}
+\def\@dfncountersep{.}
+\def\@begindefinition#1#2{\trivlist
+   \item[\hskip\labelsep{\bfseries #1\ #2.}]\upshape}
+\def\@opargbegindefinition#1#2#3{\trivlist
+      \item[\hskip\labelsep{\bfseries #1\ #2\ (#3).}]\upshape}
+\def\@enddefinition{\endtrivlist}
+
+\def\@begintheorem#1#2{\trivlist
+  \let\baselinestretch\@blstr
+   \item[\hskip \labelsep{\bfseries #1\ #2.}]\itshape}
+\def\@opargbegintheorem#1#2#3{\trivlist
+  \let\baselinestretch\@blstr
+      \item[\hskip \labelsep{\bfseries #1\ #2\ (#3).}]\itshape}
+
+\def\newproof#1{%
+  \@ifnextchar[{\@oprf{#1}}{\@nprf{#1}}}
+\def\@nprf#1#2{%
+  \@ifnextchar[{\@xnprf{#1}{#2}}{\@ynprf{#1}{#2}}}
+\def\@xnprf#1#2[#3]{%
+  \expandafter\@ifdefinable\csname #1\endcsname
+    {\@definecounter{#1}\@newctr{#1}[#3]%
+     \expandafter\xdef\csname the#1\endcsname{%
+       \expandafter\noexpand\csname the#3\endcsname \@prfcountersep
+          \@prfcounter{#1}}%
+     \global\@namedef{#1}{\@prf{#1}{#2}}%
+     \global\@namedef{end#1}{\@endproof}}}
+\def\@ynprf#1#2{%
+  \expandafter\@ifdefinable\csname #1\endcsname
+    {\@definecounter{#1}%
+     \expandafter\xdef\csname the#1\endcsname{\@prfcounter{#1}}%
+     \global\@namedef{#1}{\@prf{#1}{#2}}%
+     \global\@namedef{end#1}{\@endproof}}}
+\def\@oprf#1[#2]#3{%
+  \@ifundefined{c@#2}{\@nocounterr{#2}}%
+    {\expandafter\@ifdefinable\csname #1\endcsname
+    {\global\@namedef{the#1}{\@nameuse{the#2}}%
+  \global\@namedef{#1}{\@prf{#2}{#3}}%
+  \global\@namedef{end#1}{\@endproof}}}}
+\def\@prf#1#2{%
+  \refstepcounter{#1}%
+  \@ifnextchar[{\@yprf{#1}{#2}}{\@xprf{#1}{#2}}}
+\def\@xprf#1#2{%
+  \@beginproof{#2}{\csname the#1\endcsname}\ignorespaces}
+\def\@yprf#1#2[#3]{%
+  \@opargbeginproof{#2}{\csname the#1\endcsname}{#3}\ignorespaces}
+\def\@prfcounter#1{\noexpand\arabic{#1}}
+\def\@prfcountersep{.}
+\def\@beginproof#1#2{\trivlist\let\baselinestretch\@blstr
+   \item[\hskip \labelsep{\scshape #1.}]\rmfamily}
+\def\@opargbeginproof#1#2#3{\trivlist\let\baselinestretch\@blstr
+      \item[\hskip \labelsep{\scshape #1\ (#3).}]\rmfamily}
+\def\@endproof{\endtrivlist}
+\newcommand*{\qed}{\hbox{}\hfill$\Box$}
+
+\@ifundefined{@biboptions}{\xdef\@biboptions{numbers}}{}
+\InputIfFileExists{\jobname.spl}{}{}
+\RequirePackage[\@biboptions]{natbib}
+
+\newwrite\splwrite
+\immediate\openout\splwrite=\jobname.spl
+\def\biboptions#1{\def\next{#1}\immediate\write\splwrite{%
+   \string\g@addto@macro\string\@biboptions{%
+    ,\expandafter\strip@prefix\meaning\next}}}
+
+\let\baselinestretch=\@blstr
+
+\ifnum\jtype=1
+ \RequirePackage{geometry}
+ \geometry{twoside,
+  paperwidth=210mm,
+  paperheight=297mm,
+  textheight=562pt,
+  textwidth=384pt,
+  centering,
+  headheight=50pt,
+  headsep=12pt,
+  footskip=12pt,
+  footnotesep=24pt plus 2pt minus 12pt,
+ }
+ \global\let\bibfont=\footnotesize
+ \global\bibsep=0pt
+ \if@twocolumn\global\@twocolumnfalse\fi
+\else\ifnum\jtype=3
+ \RequirePackage{geometry}
+ \geometry{twoside,
+  paperwidth=210mm,
+  paperheight=297mm,
+  textheight=622pt,
+  textwidth=468pt,
+  centering,
+  headheight=50pt,
+  headsep=12pt,
+  footskip=18pt,
+  footnotesep=24pt plus 2pt minus 12pt,
+  columnsep=2pc
+ }
+ \global\let\bibfont=\footnotesize
+ \global\bibsep=0pt
+ \if@twocolumn\input{fleqn.clo}\fi
+\else\ifnum\jtype=5
+ \RequirePackage{geometry}
+ \geometry{twoside,
+  paperwidth=210mm,
+  paperheight=297mm,
+  textheight=682pt,
+  textwidth=522pt,
+  centering,
+ headheight=50pt,
+  headsep=12pt,
+  footskip=18pt,
+  footnotesep=24pt plus 2pt minus 12pt,
+  columnsep=18pt
+ }%
+ \global\let\bibfont=\footnotesize
+ \global\bibsep=0pt
+ \input{fleqn.clo}
+ \global\@twocolumntrue
+%%
+%% End of option '5p'
+%%
+\fi\fi\fi
+\def\journal#1{\gdef\@journal{#1}}
+ \let\@journal\@empty
+\newenvironment{frontmatter}{}{\maketitle}
+
+\long\def\@makecaption#1#2{%
+  \vskip\abovecaptionskip\footnotesize
+  \sbox\@tempboxa{#1: #2}%
+  \ifdim \wd\@tempboxa >\hsize
+    #1: #2\par
+  \else
+    \global \@minipagefalse
+    \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}%
+  \fi
+  \vskip\belowcaptionskip}
+
+\AtBeginDocument{\@ifpackageloaded{hyperref}
+  {\def\@linkcolor{blue}
+   \def\@anchorcolor{blue}
+   \def\@citecolor{blue}
+   \def\@filecolor{blue}
+   \def\@urlcolor{blue}
+   \def\@menucolor{blue}
+   \def\@pagecolor{blue}
+\begingroup
+  \@makeother\`%
+  \@makeother\=%
+  \edef\x{%
+    \edef\noexpand\x{%
+      \endgroup
+      \noexpand\toks@{%
+        \catcode 96=\noexpand\the\catcode`\noexpand\`\relax
+        \catcode 61=\noexpand\the\catcode`\noexpand\=\relax
+      }%
+    }%
+    \noexpand\x
+  }%
+\x
+\@makeother\`
+\@makeother\=
+}{}}
+%%
+\def\appendixname{Appendix }
+\renewcommand\appendix{\par
+  \setcounter{section}{0}%
+  \setcounter{subsection}{0}%
+  \setcounter{equation}{0}
+  \gdef\thefigure{\@Alph\c@section.\arabic{figure}}%
+  \gdef\thetable{\@Alph\c@section.\arabic{table}}%
+  \gdef\thesection{\appendixname~\@Alph\c@section}%
+  \@addtoreset{equation}{section}%
+  \gdef\theequation{\@Alph\c@section.\arabic{equation}}%
+  \addtocontents{toc}{\string\let\string\numberline\string\tmptocnumberline}{}{}
+}
+
+%%%% \numberline width calculation for appendix.
+\newdimen\appnamewidth
+\def\tmptocnumberline#1{%
+   \setbox0=\hbox{\appendixname}
+   \appnamewidth=\wd0
+   \addtolength\appnamewidth{2.5pc}
+   \hb@xt@\appnamewidth{#1\hfill}
+}
+
+%% Added for work with amsrefs.sty
+
+\@ifpackageloaded{amsrefs}%
+  {}
+  {%\let\bibsection\relax%
+  \AtBeginDocument{\def\cites@b#1#2,#3{%
+    \begingroup[%
+        \toks@{\InnerCite{#2}#1}%
+        \ifx\@empty#3\@xp\@gobble\fi
+        \cites@c#3%
+}}}
+%%
+%% Added for avoiding clash with cleveref.sty
+
+\@ifpackageloaded{cleveref}%
+ {}
+ {\def\tnotetext[#1]#2{\g@addto@macro\@tnotes{%
+    \refstepcounter{tnote}%
+    \immediate\write\@auxout{\string\Newlabel{#1}{\thetnote}}
+    \def\thefootnote{\ifcase\c@tnote\or\ding{73}\or\ding{73}\ding{73}\fi}%
+    \footnotetext{#2}}}
+%%%
+  \def\fntext[#1]#2{\g@addto@macro\@fnotes{%
+    \refstepcounter{fnote}%
+    \immediate\write\@auxout{\string\Newlabel{#1}{\thefnote}}
+    \def\thefootnote{\thefnote}%
+    \global\setcounter{footnote}{\thefnote}%
+    \footnotetext{#2}}}
+%%%
+  \def\cortext[#1]#2{\g@addto@macro\@cornotes{%
+    \refstepcounter{cnote}%
+    \immediate\write\@auxout{\string\Newlabel{#1}{\thecnote}}
+    \def\thefootnote{\ifcase\thecnote\or$\ast$\or
+    $\ast\ast$\fi}%
+    \footnotetext{#2}}}
+}
+\endinput
+%%
+%% End of file `elsarticle.cls'.
+
-- 
2.39.5