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+\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 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 @@ -\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} +\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} 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