-@article{Dirac1953888,\r
- title = "The lorentz transformation and absolute time",\r
- journal = "Physica ",\r
- volume = "19",\r
- number = "1-–12",\r
- pages = "888--896",\r
- year = "1953",\r
- doi = "10.1016/S0031-8914(53)80099-6",\r
- author = "P.A.M. Dirac"\r
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-\r
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- title = "The theory of a general quantum system interacting with a linear dissipative system",\r
- journal = "Annals of Physics ",\r
- volume = "24",\r
- pages = "118--173",\r
- year = "1963",\r
- doi = "10.1016/0003-4916(63)90068-X",\r
- author = "R.P Feynman AND F.L {Vernon Jr.}"\r
-}\r
-\r
-@Article{Aberth73,\r
- title = "Iteration Methods for Finding all Zeros of a Polynomial Simultaneously",\r
- journal = "Mathematics of Computation",\r
- volume = "27",\r
- number = "122",\r
- pages = "339--344",\r
- year = "1973",\r
- doi = "10.1016/0003-4916(63)90068-X",\r
- author = "O. Aberth",\r
- \r
-}x\r
-\r
-\r
-@Article{Ilie50,\r
- title = "On the approximations of Newton",\r
- journal = "Annual Sofia Univ",\r
- volume = "",\r
- number = "46",\r
- pages = "167--171",\r
- year = "1950",\r
- doi = "10.1016/0003-4916(63)90068-X",\r
- author = "L. Ilieff",\r
- \r
-}x\r
-@Article{Docev62,\r
- title = "An alternative method of Newton for simultaneous calculation of all the roots of a given algebraic equation",\r
- journal = "Phys. Math. J",\r
- volume = "",\r
- number = "5",\r
- pages = "136-139",\r
- year = "1962",\r
- author = "K. Docev",\r
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-\r
-@Article{Durand60,\r
- title = "Solution Numerique des Equations Algebriques, Vol. 1, Equations du Type F(x)=0, Racines d'une Polynome",\r
- journal = "",\r
- volume = "Vol.1",\r
- number = "",\r
- pages = "",\r
- year = "1960",\r
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-\r
-@Article{Kerner66,\r
- title = "Ein Gesamtschritteverfahren zur Berechnung der Nullstellen von Polynomen",\r
- journal = " ",\r
- volume = "",\r
- number = "8",\r
- pages = "290-294",\r
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-}x\r
-\r
-@Article{Borch-Supan63,\r
- title = "A posteriori error for the zeros of polynomials",\r
- journal = " ",\r
- volume = "",\r
- number = "5",\r
- pages = "380-398",\r
- year = "1963",\r
- author = "W. Borch-Supan",\r
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-\r
-@Article{Ehrlich67,\r
- title = "A modified Newton method for polynomials",\r
- journal = " Comm. Ass. Comput. Mach.",\r
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- number = "10",\r
- pages = "107-108",\r
- year = "1967",\r
- author = "L.W. Ehrlich",\r
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- journal = " Intern. J. Computer Math",\r
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- number = "14",\r
- pages = "45-58",\r
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- author = "G. Loizon",\r
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-\r
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- journal = " Parallel Computing",\r
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- pages = "351-358",\r
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- author = "T.L. Freeman",\r
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-@Article{Freemanall90,\r
- title = " Asynchronous polynomial zero-finding algorithms",\r
- journal = " Parallel Computing",\r
- volume = "",\r
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- pages = "673-681",\r
- year = "1990",\r
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- title = " Extraction de racines dans des polynômes creux de degrées élevés.RSRCP (Réseaux et Systèmes Répartis, Calculateurs Parallèles)",\r
- journal = " Algorithmes itératifs paralléles et distribués",\r
- volume = "1",\r
- number = "13",\r
- pages = "67-81",\r
- year = "1990",\r
- author = "R. Couturier AND F. Spetiri",\r
-}x\r
-\r
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- title = " On a Theorem by J.L. Walsh Concerning the Moduli of Roots of Algebraic Equations,Bull. A.M.S.",\r
- journal = " Algorithmes itératifs paralléles et distribués",\r
- volume = "1",\r
- number = "47",\r
- pages = "742-746",\r
- year = "1941",\r
- author = "A. Ostrowski",\r
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-\r
-\r
-@Manual{CUDA10,\r
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- journal = " IEEE. Conf. on advanced Networking, Distributed Systems and Applications",\r
- volume = "",\r
- number = "",\r
- pages = "53-57",\r
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- title = " Perfectionnements de la méthode asynchrone de Durand-Kerner pour les polynômes complexes",\r
- journal = " Calculateurs Parallèles",\r
- volume = "10",\r
- number = "4",\r
- pages = "449-458",\r
- year = "1998",\r
- author = "K. Rhofir AND F. Spies AND Jean-Claude Miellou",\r
-}x\r
-\r
-@Article{Bini96,\r
- \r
- title = " Numerical computation of polynomial zeros by means of Aberth s method",\r
- journal = " Numerical Algorithms",\r
- volume = "13",\r
- number = "4",\r
- pages = "179-200",\r
- year = "1996",\r
- author = "D. Bini",\r
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-\r
-@Article{Mirankar68,\r
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- journal = " IBM Res Dev",\r
- volume = "30",\r
- number = "",\r
- pages = "297-301",\r
- year = "1968",\r
- author = "WL. Mirankar",\r
-}x\r
-\r
-@Article{Mirankar71,\r
- title = " A survey of parallelism in numerical analysis",\r
- journal = " SIAM Rev",\r
- volume = "",\r
- number = "",\r
- pages = "524-547",\r
- year = "1971",\r
- author = "WL. Mirankar",\r
-}x\r
-\r
-@Article{Schedler72,\r
- title = " Parallel iteration methods in complexity of computer communications",\r
- journal = " Commun ACM ",\r
- volume = "",\r
- number = "",\r
- pages = "286-290",\r
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- author = "GS. Schedler",\r
-}x\r
-\r
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- title = " Parallel iteration methods in complexity of computer communications",\r
- journal = " Plenum, New York",\r
- volume = "",\r
- number = "",\r
- pages = "",\r
- year = "1972",\r
- author = "S. Winogard",\r
-}x\r
-\r
-@Article{Benall68,\r
- title = " A fast parallel algorithm for determining all roots of a polynomial with real roots",\r
- journal = " Int: Proc of ACM",\r
- volume = "",\r
- number = "",\r
- pages = "340-349",\r
- year = "1968",\r
- author = "M. Ben-Or AND E. Feig AND D. Kozzen AND P. Tiwary",\r
-}x\r
-\r
-@Article{Riceall06,\r
- title = " A highly parallel algorithm for root extraction",\r
- journal = " IEEE Trans Comp",\r
- volume = "38",\r
- number = "3",\r
- pages = "443-449",\r
- year = "2006",\r
- author = "TA. Rice AND LH. Jamieson",\r
-}x\r
-\r
-@Article{Cosnard90,\r
- title = " Finding the roots of a polynomial on an MIMD multicomputer",\r
- journal = " Parallel Comput",\r
- volume = "15",\r
- number = "3",\r
- pages = "75-85",\r
- year = "1990",\r
- author = "M. Cosnard AND P. Fraigniaud",\r
-}x\r
-\r
-@Article{Janall99,\r
- title = " Efficient parallel algorithms for finding polynomial zeroes",\r
- journal = "Proc of the 6th int conference on advance computing, CDAC, Pune University Campus,India",\r
- volume = "15",\r
- number = "3",\r
- pages = "189-196",\r
- year = "1999",\r
- author = "PK. Jana AND BP. Sinha AND R. Datta Gupta",\r
-}x\r
-\r
-@Article{Jana06,\r
- title = " Polynomial interpolation and polynomial root finding on OTIS-Mesh",\r
- journal = " Parallel Comput",\r
- volume = "32",\r
- number = "3",\r
- pages = "301-312",\r
- year = "2006",\r
- author = "PK. Jana",\r
-}x\r
-@Article{Kalantari08,\r
- title = " Polynomial root finding and polynomiography.",\r
- journal = " World Scientifict,New Jersey",\r
- volume = "",\r
- number = "",\r
- pages = "",\r
- year = "",\r
- author = "B. Kalantari",\r
-}x\r
-\r
-@Article{Gemignani07,\r
- title = " Structured matrix methods for polynomial root finding.",\r
- journal = " n: Proc of the 2007 Intl symposium on symbolic and algebraic computation",\r
- volume = "",\r
- number = "",\r
- pages = "175-180",\r
- year = "2007",\r
- author = "L. Gemignani",\r
-}x\r
-\r
-\r
-\r
-@Article{Skachek08,\r
- title = " Structured matrix methods for polynomial root finding.",\r
- journal = " n: Proc of the 2007 Intl symposium on symbolic and algebraic computation",\r
- volume = "",\r
- number = "",\r
- pages = "175-180",\r
- year = "2008",\r
- author = "V. Skachek",\r
-}x\r
-\r
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- AUTHOR = {V. Skachek},\r
- editor = {\7f},\r
- TITLE = {Probabilistic algorithm for finding roots of linearized polynomials},\r
- PUBLISHER = {codes and cryptography. Kluwer},\r
- YEAR = {2008},\r
- volume = {\7f},\r
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- series = {\7f},\r
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-}x\r
-\r
-@Article{Zhancall08,\r
- title = " A constrained learning algorithm for finding multiple real roots of polynomial",\r
- journal = " In: Proc of the 2008 intl symposium on computational intelligence and design",\r
- volume = "",\r
- number = "",\r
- pages = "38-41",\r
- year = "2008",\r
- author = "X. Zhanc AND M. Wan,Z.Yi",\r
-}x\r
-\r
-\r
-@Article{Zhuall08,\r
- title = " an adaptive algorithm finding multiple roots of polynomials",\r
- journal = " Lect Notes Comput Sci ",\r
- volume = "",\r
- number = "5262",\r
- pages = "674-681",\r
- year = "2008",\r
- author = "W. Zhu AND w. Zeng AND D. Lin",\r
-}x\r
-@Article{Azad07,\r
- title = " The performance of synchronous parallel polynomial root extraction on a ring multicomputer",\r
- journal = " Clust Comput ",\r
- volume = "2",\r
- number = "10",\r
- pages = "167-174",\r
- year = "2007",\r
- author = "HS. Azad",\r
-}x\r
-\r
-\r
-\r
-\r
-@Article{Bini04,\r
- title = " Inverse power and Durand Kerner iterations for univariate polynomial root finding",\r
- journal = " Comput Math Appl ",\r
- volume = "",\r
- number = "47",\r
- pages = "447-459",\r
- year = "2004",\r
- author = "DA. Bini AND L. Gemignani",\r
-}x\r
-\r
-@Article{Jana99,\r
- title = " Finding polynomial zeroes on a Multi-mesh of trees (MMT)",\r
- journal = " In: Proc of the 2nd int conference on information technology",\r
- volume = "",\r
- number = "",\r
- pages = "202-206",\r
- year = "1999",\r
- author = "PK. Jana",\r
-}x\r
-\r
-@Article{Weierstrass03,\r
- title = " Neuer Beweis des Satzes, dass jede ganze rationale function einer veranderlichen dagestellt werden kann als ein product aus linearen functionen derselben veranderlichen",\r
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- volume = "3",\r
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-\r
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- YEAR = {2015},\r
- volume = {7},\r
- number = {02829},\r
- series = {001},\r
- month = {march},\r
-}x\r
+@article{Dirac1953888,
+ title = "The lorentz transformation and absolute time",
+ journal = "Physica ",
+ volume = "19",
+ number = "1-–12",
+ pages = "888--896",
+ year = "1953",
+ doi = "10.1016/S0031-8914(53)80099-6",
+ author = "P.A.M. Dirac"
+}
+
+@article{Feynman1963118,
+ title = "The theory of a general quantum system interacting with a linear dissipative system",
+ journal = "Annals of Physics ",
+ volume = "24",
+ pages = "118--173",
+ year = "1963",
+ doi = "10.1016/0003-4916(63)90068-X",
+ author = "R.P Feynman AND F.L {Vernon Jr.}"
+}
+
+@Article{Aberth73,
+ title = "Iteration Methods for Finding all Zeros of a Polynomial Simultaneously",
+ journal = "Mathematics of Computation",
+ volume = "27",
+ number = "122",
+ pages = "339--344",
+ year = "1973",
+ doi = "10.1016/0003-4916(63)90068-X",
+ author = "O. Aberth",
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+}x
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+
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+ journal = "Annual Sofia Univ",
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+ number = "46",
+ pages = "167--171",
+ year = "1950",
+ doi = "10.1016/0003-4916(63)90068-X",
+ author = "L. Ilieff",
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+}x
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+ title = "An alternative method of Newton for simultaneous calculation of all the roots of a given algebraic equation",
+ journal = "Phys. Math. J",
+ volume = "",
+ number = "5",
+ pages = "136-139",
+ year = "1962",
+ author = "K. Docev",
+}x
+
+@Article{Durand60,
+ title = "Solution Numerique des Equations Algebriques, Vol. 1, Equations du Type F(x)=0, Racines d'une Polynome",
+ journal = "",
+ volume = "Vol.1",
+ number = "",
+ pages = "",
+ year = "1960",
+ author = "E. Durand",
+}x
+
+@Article{Kerner66,
+ title = "Ein Gesamtschritteverfahren zur Berechnung der Nullstellen von Polynomen",
+ journal = " ",
+ volume = "",
+ number = "8",
+ pages = "290-294",
+ year = "1966",
+ author = "I. Kerner",
+}x
+
+@Article{Borch-Supan63,
+ title = "A posteriori error for the zeros of polynomials",
+ journal = " ",
+ volume = "",
+ number = "5",
+ pages = "380-398",
+ year = "1963",
+ author = "W. Borch-Supan",
+}x
+
+@Article{Ehrlich67,
+ title = "A modified Newton method for polynomials",
+ journal = " Comm. Ass. Comput. Mach.",
+ volume = "",
+ number = "10",
+ pages = "107-108",
+ year = "1967",
+ author = "L.W. Ehrlich",
+}x
+
+@Article{Loizon83,
+ title = "Higher-order iteration functions for simultaneously approximating polynomial zeros",
+ journal = " Intern. J. Computer Math",
+ volume = "",
+ number = "14",
+ pages = "45-58",
+ year = "1983",
+ author = "G. Loizon",
+}x
+
+@Article{Freeman89,
+ title = " Calculating polynomial zeros on a local memory parallel computer",
+ journal = " Parallel Computing",
+ volume = "",
+ number = "12",
+ pages = "351-358",
+ year = "1989",
+ author = "T.L. Freeman",
+}x
+
+@Article{Freemanall90,
+ title = " Asynchronous polynomial zero-finding algorithms",
+ journal = " Parallel Computing",
+ volume = "",
+ number = "17",
+ pages = "673-681",
+ year = "1990",
+ author = "T.L. Freeman AND R.K. Brankin",
+}x
+
+@Article{Raphaelall01,
+ title = " Extraction de racines dans des polynômes creux de degrées élevés.RSRCP (Réseaux et Systèmes Répartis, Calculateurs Parallèles)",
+ journal = " Algorithmes itératifs paralléles et distribués",
+ volume = "1",
+ number = "13",
+ pages = "67-81",
+ year = "1990",
+ author = "R. Couturier AND F. Spiteri",
+}x
+
+@Article{Ostrowski41,
+ title = " On a Theorem by J.L. Walsh Concerning the Moduli of Roots of Algebraic Equations,Bull. A.M.S.",
+ journal = " Algorithmes itératifs paralléles et distribués",
+ volume = "1",
+ number = "47",
+ pages = "742-746",
+ year = "1941",
+ author = "A. Ostrowski",
+}x
+
+
+@Manual{CUDA10,
+title = {Compute Unified Device Architecture Programming Guide Version 3.0},
+OPTkey = {NVIDIA CUDA},
+OPTauthor = {•},
+OPTorganization = {NVIDIA CUDA},
+OPTaddress = {•},
+OPTedition = {•},
+OPTmonth = {March},
+OPTyear = {2010},
+OPTnote = {http://www.nvidia.com/object/cuda_develop.html},
+OPTannote = {•}
+}
+
+@Article{Kahinall14,
+ title = " parallel implementation of the Durand-Kerner algorithm for polynomial root-finding on GPU",
+ journal = " IEEE. Conf. on advanced Networking, Distributed Systems and Applications",
+ volume = "",
+ number = "",
+ pages = "53-57",
+ year = "2014",
+ author = "K. Ghidouche AND R. Couturier AND A. Sider",
+}x
+
+@Article{Karimall98,
+
+ title = " Perfectionnements de la méthode asynchrone de Durand-Kerner pour les polynômes complexes",
+ journal = " Calculateurs Parallèles",
+ volume = "10",
+ number = "4",
+ pages = "449-458",
+ year = "1998",
+ author = "K. Rhofir AND F. Spies AND Jean-Claude Miellou",
+}x
+
+@Article{Bini96,
+
+ title = " Numerical computation of polynomial zeros by means of Aberth s method",
+ journal = " Numerical Algorithms",
+ volume = "13",
+ number = "4",
+ pages = "179-200",
+ year = "1996",
+ author = "D. Bini",
+}x
+
+@Article{Mirankar68,
+ title = " Parallel methods for approximating the roots of a function",
+ journal = " IBM Res Dev",
+ volume = "30",
+ number = "",
+ pages = "297-301",
+ year = "1968",
+ author = "WL. Mirankar",
+}x
+
+@Article{Mirankar71,
+ title = " A survey of parallelism in numerical analysis",
+ journal = " SIAM Rev",
+ volume = "",
+ number = "",
+ pages = "524-547",
+ year = "1971",
+ author = "WL. Mirankar",
+}x
+
+@Article{Schedler72,
+ title = " Parallel iteration methods in complexity of computer communications",
+ journal = " Commun ACM ",
+ volume = "",
+ number = "",
+ pages = "286-290",
+ year = "1967",
+ author = "GS. Schedler",
+}x
+
+@Article{Winogard72,
+ title = " Parallel iteration methods in complexity of computer communications",
+ journal = " Plenum, New York",
+ volume = "",
+ number = "",
+ pages = "",
+ year = "1972",
+ author = "S. Winogard",
+}x
+
+@Article{Benall68,
+ title = " A fast parallel algorithm for determining all roots of a polynomial with real roots",
+ journal = " Int: Proc of ACM",
+ volume = "",
+ number = "",
+ pages = "340-349",
+ year = "1968",
+ author = "M. Ben-Or AND E. Feig AND D. Kozzen AND P. Tiwary",
+}x
+
+@Article{Riceall06,
+ title = " A highly parallel algorithm for root extraction",
+ journal = " IEEE Trans Comp",
+ volume = "38",
+ number = "3",
+ pages = "443-449",
+ year = "2006",
+ author = "TA. Rice AND LH. Jamieson",
+}x
+
+@Article{Cosnard90,
+ title = " Finding the roots of a polynomial on an MIMD multicomputer",
+ journal = " Parallel Comput",
+ volume = "15",
+ number = "3",
+ pages = "75-85",
+ year = "1990",
+ author = "M. Cosnard AND P. Fraigniaud",
+}x
+
+@Article{Janall99,
+ title = " Efficient parallel algorithms for finding polynomial zeroes",
+ journal = "Proc of the 6th int conference on advance computing, CDAC, Pune University Campus,India",
+ volume = "15",
+ number = "3",
+ pages = "189-196",
+ year = "1999",
+ author = "PK. Jana AND BP. Sinha AND R. Datta Gupta",
+}x
+
+@Article{Jana06,
+ title = " Polynomial interpolation and polynomial root finding on OTIS-Mesh",
+ journal = " Parallel Comput",
+ volume = "32",
+ number = "3",
+ pages = "301-312",
+ year = "2006",
+ author = "PK. Jana",
+}x
+@Article{Kalantari08,
+ title = " Polynomial root finding and polynomiography.",
+ journal = " World Scientifict,New Jersey",
+ volume = "",
+ number = "",
+ pages = "",
+ year = "",
+ author = "B. Kalantari",
+}x
+
+@Article{Gemignani07,
+ title = " Structured matrix methods for polynomial root finding.",
+ journal = " n: Proc of the 2007 Intl symposium on symbolic and algebraic computation",
+ volume = "",
+ number = "",
+ pages = "175-180",
+ year = "2007",
+ author = "L. Gemignani",
+}x
+
+
+
+@Article{Skachek08,
+ title = " Structured matrix methods for polynomial root finding.",
+ journal = " n: Proc of the 2007 Intl symposium on symbolic and algebraic computation",
+ volume = "",
+ number = "",
+ pages = "175-180",
+ year = "2008",
+ author = "V. Skachek",
+}x
+
+@BOOK{Skachek008,
+ AUTHOR = {V. Skachek},
+ editor = {\7f},
+ TITLE = {Probabilistic algorithm for finding roots of linearized polynomials},
+ PUBLISHER = {codes and cryptography. Kluwer},
+ YEAR = {2008},
+ volume = {\7f},
+ number = {\7f},
+ series = {\7f},
+ address = {\7f},
+ edition = {Design},
+ month = {\7f},
+ note = {\7f},
+ abstract = {\7f},
+ isbn = {\7f},
+ price = {\7f},
+ keywords = {\7f},
+ source = {\7f},
+}x
+
+@Article{Zhancall08,
+ title = " A constrained learning algorithm for finding multiple real roots of polynomial",
+ journal = " In: Proc of the 2008 intl symposium on computational intelligence and design",
+ volume = "",
+ number = "",
+ pages = "38-41",
+ year = "2008",
+ author = "X. Zhanc AND M. Wan,Z.Yi",
+}x
+
+
+@Article{Zhuall08,
+ title = " an adaptive algorithm finding multiple roots of polynomials",
+ journal = " Lect Notes Comput Sci ",
+ volume = "",
+ number = "5262",
+ pages = "674-681",
+ year = "2008",
+ author = "W. Zhu AND w. Zeng AND D. Lin",
+}x
+@Article{Azad07,
+ title = " The performance of synchronous parallel polynomial root extraction on a ring multicomputer",
+ journal = " Clust Comput ",
+ volume = "2",
+ number = "10",
+ pages = "167-174",
+ year = "2007",
+ author = "HS. Azad",
+}x
+
+
+
+
+@Article{Bini04,
+ title = " Inverse power and Durand Kerner iterations for univariate polynomial root finding",
+ journal = " Comput Math Appl ",
+ volume = "",
+ number = "47",
+ pages = "447-459",
+ year = "2004",
+ author = "DA. Bini AND L. Gemignani",
+}x
+
+@Article{Jana99,
+ title = " Finding polynomial zeroes on a Multi-mesh of trees (MMT)",
+ journal = " In: Proc of the 2nd int conference on information technology",
+ volume = "",
+ number = "",
+ pages = "202-206",
+ year = "1999",
+ author = "PK. Jana",
+}x
+
+@Article{Weierstrass03,
+ title = " Neuer Beweis des Satzes, dass jede ganze rationale function einer veranderlichen dagestellt werden kann als ein product aus linearen functionen derselben veranderlichen",
+ journal = " Ges. Werke",
+ volume = "3",
+ number = "",
+ pages = "251-269",
+ year = "1903",
+ author = "K. Weierstrass",
+}x
+
+
+
+@BOOK{NVIDIA10,
+ AUTHOR = {NVIDIA},
+ editor = {Design Guide},
+ TITLE = {NVIDIA CUDA C Programming Guide},
+ PUBLISHER = {PG},
+ YEAR = {2015},
+ volume = {7},
+ number = {02829},
+ series = {001},
+ month = {march},
+}x
