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- year = "1953",
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- author = "P.A.M. Dirac"
-}
-
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- 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",
number = "122",
pages = "339--344",
year = "1973",
- doi = "10.1016/0003-4916(63)90068-X",
author = "O. Aberth",
}x
-
@Article{Ilie50,
title = "On the approximations of Newton",
journal = "Annual Sofia Univ",
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+ volume = "46",
+ number = "",
pages = "167--171",
year = "1950",
- doi = "10.1016/0003-4916(63)90068-X",
- author = "L. Ilieff",
+ author = "L. Ilieff",
}x
+
@Article{Docev62,
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",
+ volume = "5",
+ number = "",
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
@Book{Durand60,
author = "\'E. Durand",
publisher = "Masson, Paris",
year = "1960",
}x
-%@Article{Kerner66,
- %title = "Ein Gesamtschritteverfahren zur Berechnung der Nullstellen von Polynomen",
- % journal = "Numerische Mathematik",
-% volume = "8",
-% number = "3",
-% pages = "290-294",
- %year = "1966",
- % author = "I. Kerner",
-%}x
-
-
@Article{Kerner66,
author = "Immo O. Kerner",
title = "{Ein Gesamtschrittverfahren zur Berechnung der
journal-url = "http://link.springer.com/journal/211",
language = "German",
}
-%@Article{Borch-Supan63,
-% title = "A posteriori error for the zeros of polynomials",
- %journal = " Numerische Mathematik",
- % volume = "5",
-% number = "",
-% pages = "380-398",
- %year = "1963",
- % author = "W. Borch-Supan",
-%}x
@Article{Borch-Supan63,
author = "W. Boersch-Supan",
Calgary, Alberta T2N 1N4, Canada",
}
-%@Article{Ehrlich67,
-% title = "A modified Newton method for polynomials",
-% journal = " Comm. Ass. Comput. Mach.",
-% volume = "10",
-% number = "2",
-% pages = "107-108",
- %year = "1967",
- % author = "L.W. Ehrlich",
-%}x
-
@Article{Ehrlich67,
title = "A modified Newton method for polynomials",
author = "Louis W. Ehrlich",
title = "Higher-order iteration functions for simultaneously approximating polynomial zeros",
journal = " Intern. J. Computer Math",
volume = "14",
- number = "",
+ number = "1",
pages = "45-58",
year = "1983",
- author = "G. Loizon",
+ author = "G. Loizou",
}x
@Article{Freeman89,
- title = " Calculating polynomial zeros on a local memory parallel computer",
- journal = " Parallel Computing",
- volume = "12",
- number = "",
- pages = "351-358",
- year = "1989",
- author = "T.L. Freeman",
-}x
-
+ title = "Calculating polynomial zeros on a local memory
+ parallel computer",
+ author = "T. L. Freeman",
+ journal = "Parallel Computing",
+ year = "1989",
+ number = "3",
+ volume = "12",
+ bibdate = "2011-09-09",
+ bibsource = "DBLP,
+ http://dblp.uni-trier.de/db/journals/pc/pc12.html#Freeman89",
+ pages = "351--358",
+ URL = "http://dx.doi.org/10.1016/0167-8191(89)90093-8",
+}
@Article{Freemanall90,
title = " Asynchronous polynomial zero-finding algorithms",
journal = " Parallel Computing",
}x
@Article{Raphaelall01,
- title = " Extraction de racines dans des polynômes creux de degrées élevés. RSRCP (Réseaux et Systèmes Répartis, Calculateurs Parallèles)",
+ 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",
}x
@Article{Ostrowski41,
- title = " On a Theorem by J.L. Walsh Concerning the Moduli of Roots of Algebraic Equations,Bull. A.M.S.",
+ title = " On a Theorem by {J. L. Walsh} Concerning the Moduli of Roots of Algebraic Equations. A.M.S.",
journal = " Algorithmes itératifs paralléles et distribués",
volume = "1",
number = "47",
}
@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",
+ title = "Parallel implementation of the {D}urand-{K}erner algorithm for polynomial root-finding on {GPU}",
+ journal = "IEEE. Conf. on advanced Networking, Distributed Systems and Applications",
volume = "",
number = "",
pages = "53-57",
@Article{Karimall98,
- title = " Perfectionnements de la méthode asynchrone de Durand-Kerner pour les polynômes complexes",
+ title = " Perfectionnements de la méthode asynchrone de {D}urand-{K}erner pour les polynômes complexes",
journal = " Calculateurs Parallèles",
volume = "10",
number = "4",
}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
-
+ title = "Numerical computation of polynomial zeros by means of
+ Aberth's method",
+ author = "D. Bini",
+ journal = "Numerical Algorithms",
+ year = "1996",
+ number = "2",
+ volume = "13",
+ bibdate = "2015-09-27",
+ bibsource = "DBLP,
+ http://dblp.uni-trier.de/db/journals/na/na13.html#Bini96",
+ pages = "179--200",
+ URL = "http://dx.doi.org/10.1007/BF02207694",
+}
@Article{Mirankar68,
title = " Parallel methods for approximating the roots of a function",
journal = " IBM Res Dev",
- volume = "30",
+ volume = "13",
number = "",
pages = "297-301",
year = "1968",
@Article{Mirankar71,
title = " A survey of parallelism in numerical analysis",
journal = " SIAM Rev",
- volume = "",
+ volume = "13",
number = "",
pages = "524-547",
year = "1971",
}x
@Article{Schedler72,
- title = " Parallel iteration methods in complexity of computer communications",
+ title = " Parallel Numerical Methods for Solution of Equations",
journal = " Commun ACM ",
- volume = "",
+ volume = "10",
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",
+@InProceedings{Winogard72,
+ title = "Parallel Iteration Methods",
+ author = "S. Winograd",
+ bibdate = "2011-09-13",
+ bibsource = "DBLP,
+ http://dblp.uni-trier.de/db/conf/coco/cocc1972.html#Winograd72",
+ booktitle = "Complexity of Computer Computations",
+ publisher = "Plenum Press, New York",
+ year = "1972",
+ editor = "Raymond E. Miller and James W. Thatcher",
+ ISBN = "0-306-30707-3",
+ pages = "53--60",
+ series = "The IBM Research Symposia Series",
}x
@Article{Benall68,
volume = "",
number = "",
pages = "340-349",
- year = "1968",
+ year = "1988",
author = "M. Ben-Or AND E. Feig AND D. Kozzen AND P. Tiwary",
}x
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
+@Book{Kalantari08,
+author = {B. Kalantari},
+title = {Polynomial root finding and polynomiography},
+publisher = {World Scientifict},
+year = {2008},
+OPTkey = {•},
+OPTvolume = {•},
+OPTnumber = {•},
+OPTseries = {•},
+OPTaddress = {•},
+OPTmonth = {December},
+OPTnote = {•},
+OPTannote = {•}
+}
-@Article{Skachek08,
- title = " Structured matrix methods for polynomial root finding.",
+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 = "",
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
+
+
+@InProceedings{Gemignani07,
+ author = "L. Gemignani",
+ title = "Structured matrix methods for polynomial
+ root-finding",
+ editor = "C. W. Brown",
+ booktitle = "Proceedings of the 2007 International Symposium on
+ Symbolic and Algebraic Computation, July 29--August 1,
+ 2007, University of Waterloo, Waterloo, Ontario,
+ Canada",
+ publisher = "ACM Press",
+ address = "pub-ACM:adr",
+ ISBN = "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)",
+ isbn-13 = "978-1-59593-743-8 (print), 978-1-59593-742-1
+ (CD-ROM)",
+ pages = "175--180",
+ year = "2007",
+ doi = "http://doi.acm.org/10.1145/1277548.1277573",
+ bibdate = "Fri Jun 20 08:46:50 MDT 2008",
+ bibsource = "http://portal.acm.org/;
+ http://www.math.utah.edu/pub/tex/bib/issac.bib",
+ abstract = "In this paper we discuss the use of structured matrix
+ methods for the numerical approximation of the zeros of
+ a univariate polynomial. In particular, it is shown
+ that root-finding algorithms based on floating-point
+ eigenvalue computation can benefit from the structure
+ of the matrix problem to reduce their complexity and
+ memory requirements by an order of magnitude.",
+ acknowledgement = "Nelson H. F. Beebe, University of Utah, Department
+ of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake
+ City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1
+ 801 581 4148, e-mail: \path|beebe@math.utah.edu|,
+ \path|beebe@acm.org|, \path|beebe@computer.org|
+ (Internet), URL:
+ \path|http://www.math.utah.edu/~beebe/|",
+ keywords = "complexity; eigenvalue computation; polynomial
+ root-finding; rank-structured matrices",
+ doi-url = "http://dx.doi.org/10.1145/1277548.1277573",
+}
+
+@Article{Skachek008,
+ title = "Probabilistic algorithm for finding roots of
+ linearized polynomials",
+ author = "V. Skachek AND M. Roth",
+ journal = "Des. Codes Cryptography",
+ year = "2008",
+ number = "1",
+ volume = "46",
+ bibdate = "2008-03-11",
+ bibsource = "DBLP,
+ http://dblp.uni-trier.de/db/journals/dcc/dcc46.html#SkachekR08",
+ pages = "17--23",
+ URL = "http://dx.doi.org/10.1007/s10623-007-9125-y",
+}
@Article{Zhancall08,
title = " A constrained learning algorithm for finding multiple real roots of polynomial",
}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
+@InProceedings{Zhuall08,
+ title = "An Adaptive Algorithm Finding Multiple Roots of Polynomials",
+ author = "W. Zhu AND Z. Zeng AND Dm. Lin",
+ bibdate = "2008-09-25",
+ bibsource = "DBLP,
+ http://dblp.uni-trier.de/db/conf/isnn/isnn2008-2.html#ZhuZL08",
+ booktitle = "ISNN (2)",
+ publisher = "Springer",
+ year = "2008",
+ volume = "5264",
+ editor = "Fuchun Sun and Jianwei Zhang 0001 and Ying Tan and
+ Jinde Cao and Wen Yu 0001",
+ ISBN = "978-3-540-87733-2",
+ pages = "674--681",
+ series = "Lecture Notes in Computer Science",
+ URL = "http://dx.doi.org/10.1007/978-3-540-87734-9_77",
+}
+
@Article{Azad07,
title = " The performance of synchronous parallel polynomial root extraction on a ring multicomputer",
journal = " Clust Comput ",
@Article{Bini04,
title = " Inverse power and Durand Kerner iterations for univariate polynomial root finding",
journal = " Comput Math Appl ",
- volume = "",
- number = "47",
+ volume = "47",
+ number = "",
pages = "447-459",
year = "2004",
author = "DA. Bini AND L. Gemignani",
year = "1903",
author = "K. Weierstrass",
}x
+@Manual{NVIDIA10,
+title = {NVIDIA CUDA C Programming Guide},
+OPTkey = {•},
+OPTauthor = {NVIDIA Corporation},
+OPTorganization = {Design Guide},
+OPTaddress = {•},
+OPTedition = {•},
+OPTmonth = {march},
+OPTyear = {2015},
+OPTnote = {•},
+OPTannote = {•}
+}
-@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
