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#
# polynomialroots.bib --
#


@book{AbramowitzStegun1972,
author = {Abramowitz, M. and Stegun, I. A.},
title = {Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables},
year = {1972},
publisher= {}}

@UNPUBLISHED{wikipediaquadratic,
   title = {Quadratic Equation},
   note = {\url{http://en.wikipedia.org/wiki/Quadratic_equation}}
   }

@UNPUBLISHED{wikipediacubic,
   title = {Cubic Equation},
   note = {\url{http://en.wikipedia.org/wiki/Cubic_equation}}
   }

@UNPUBLISHED{wikipedialossofsign,
   title = {Loss of significance},
   note = {\url{http://en.wikipedia.org/wiki/Loss_of_significance}}
   }

@UNPUBLISHED{mathworldcubic,
   title = {Cubic Equation},
   note = {\url{http://mathworld.wolfram.com/CubicFormula.html}}
   }

@UNPUBLISHED{mathworldquadratic,
   title = {Quadratic Equation},
   note = {\url{http://mathworld.wolfram.com/QuadraticEquation.html}}
   }

@book{NumericalRecipes,
author = {W. H. Press and Saul A. Teukolsky and William T. Vetterling and Brian P. Flannery},
title = {Numerical Recipes in C, Second Edition},
year = {1992},
publisher= {}}

@book{WhatEveryComputerScientist,
author = {David Goldberg},
title = {What Every Computer Scientist Should Know About Floating-Point Arithmetic},
month={March},
year = {1991},
publisher= {Association for Computing Machinery, Inc.},
note = {\url{http://www.physics.ohio-state.edu/~dws/grouplinks/floating_point_math.pdf}},
}

@article{Nievergelt2003,
     jstor_articletype = {primary_article},
     title = {How (Not) to Solve Quadratic Equations},
     author = {Nievergelt, Yves},
     journal = {The College Mathematics Journal},
     jstor_issuetitle = {},
     volume = {34},
     number = {2},
     jstor_formatteddate = {Mar., 2003},
     pages = {90--104},
     url = {http://www.jstor.org/stable/3595780},
     ISSN = {07468342},
     abstract = {},
     publisher = {Mathematical Association of America},
     language = {},
     copyright = {Copyright © 2003 Mathematical Association of America},
     year = {2003},
    }

@book{FORSYTHE1991,
author = {George E. Forsythe},
title = {How Do You Solve A Quadratic Equation ?},
month={JUNE},
year = {1966},
publisher= {Computer Science Department, School of Humanities and Sciences, Stanford University},
   note = {\url{ftp://reports.stanford.edu/pub/cstr/reports/cs/tr/66/40/CS-TR-66-40.pdf}}
}

@article{Kahan2004,
     title = {On the Cost of Floating-Point Computation Without Extra-Precise Arithmetic},
     author = {W. Kahan},
     note = {\url{http://www.cs.berkeley.edu/~wkahan/Qdrtcs.pdf}},
     year = {2004},
    }

@article{Smith1962,
 author = {Smith,, Robert L.},
 title = {Algorithm 116: Complex division},
 journal = {Commun. ACM},
 volume = {5},
 number = {8},
 year = {1962},
 issn = {0001-0782},
 pages = {435},
 doi = {http://doi.acm.org/10.1145/368637.368661},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

@article{Jenkins1975,
 author = {Jenkins,, M. A.},
 title = {Algorithm 493: Zeros of a Real Polynomial [C2]},
 journal = {ACM Trans. Math. Softw.},
 volume = {1},
 number = {2},
 year = {1975},
 issn = {0098-3500},
 pages = {178--189},
 doi = {http://doi.acm.org/10.1145/355637.355643},
 publisher = {ACM},
 address = {New York, NY, USA},
 }

@article{368661,
 author = {Smith,, Robert L.},
 title = {Algorithm 116: Complex division},
 journal = {Commun. ACM},
 volume = {5},
 number = {8},
 year = {1962},
 issn = {0001-0782},
 pages = {435},
 doi = {http://doi.acm.org/10.1145/368637.368661},
 publisher = {ACM},
 address = {New York, NY, USA},
 }
@article{214414,
 author = {Stewart,, G. W.},
 title = {A note on complex division},
 journal = {ACM Trans. Math. Softw.},
 volume = {11},
 number = {3},
 year = {1985},
 issn = {0098-3500},
 pages = {238--241},
 doi = {http://doi.acm.org/10.1145/214408.214414},
 publisher = {ACM},
 address = {New York, NY, USA},
 }
@article{567808,
 author = {Li,, Xiaoye S. and Demmel,, James W. and Bailey,, David H. and Henry,, Greg and Hida,, Yozo and Iskandar,, Jimmy and Kahan,, William and Kang,, Suh Y. and Kapur,, Anil and Martin,, Michael C. and Thompson,, Brandon J. and Tung,, Teresa and Yoo,, Daniel J.},
 title = {Design, implementation and testing of extended and mixed precision BLAS},
 journal = {ACM Trans. Math. Softw.},
 volume = {28},
 number = {2},
 year = {2002},
 issn = {0098-3500},
 pages = {152--205},
 doi = {http://doi.acm.org/10.1145/567806.567808},
 publisher = {ACM},
 address = {New York, NY, USA},
 }
@article{KAHAN1987,
 author = {KAHAN, W.},
 title = {Branch cuts for complex elementary functmns, or much ado about nothing's sign bit.},
 year = {1987},
 pages = {165--211},
 publisher = {In The State of the Art m Numerzcal Analysts. Proceedings of the Joint IMA/SIAM Conference, A. Iserles and M J. D Powell, Eds. Clarendon Press, Oxford, England},
 }
@article{1039814,
 author = {Priest,, Douglas M.},
 title = {Efficient scaling for complex division},
 journal = {ACM Trans. Math. Softw.},
 volume = {30},
 number = {4},
 year = {2004},
 issn = {0098-3500},
 pages = {389--401},
 doi = {http://doi.acm.org/10.1145/1039813.1039814},
 publisher = {ACM},
 address = {New York, NY, USA},
 }
@UNPUBLISHED{schimdtnd,
   title = {Numerical Derivatives},
   note = {\url{http://fermi.la.asu.edu/PHY531/intro/node1.html}},
   author = {K.E. Schmidt}
   }
@book{dixmier,
author = {J. Dixmier, P. Dugac},
title = {Cours de Mathématiques du premier cycle, 1ère année},
year = {1969},
publisher= {Gauthier-Villars}}

@article{Forsythe1966,
 author = {George E. Forsythe},
 title = {How Do You Solve A Quadratic Equation ?},
 year = {1966},
 publisher = {TECHNICAL REPORT NO. CS40},
 note = {\url{ftp://reports.stanford.edu/pub/cstr/reports/cs/tr/66/40/CS-TR-66-40.pdf}},
 }


@ARTICLE{1667289,
title={Underflow and the Denormalized Numbers},
author={Coonen, J.T.},
journal={Computer},
year={1981},
month={March },
volume={14},
number={3},
pages={75-87},
doi={10.1109/C-M.1981.220382},
ISSN={0018-9162}, }

@book{artcomputerKnuthVol2,
author = {D. E. Knuth},
title = {The Art of Computer Programming, Volume 2, Seminumerical Algorithms},
year = {1998},
publisher= {Third Edition, Addison Wesley, Reading, MA}}

@Article{Wynn:1962:AAP,
  author =       "P. Wynn",
  title =        "An Arsenal of {ALGOL} Procedures for Complex
                 Arithmetic",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "2",
  number =       "4",
  pages =        "232--255",
  month =        dec,
  year =         "1962",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01940171",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "ftp://ftp.math.utah.edu/pub/tex/bib/bit.bib;
                 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232",
  acknowledgement = ack-nhfb,
}
@article{DBLP:journals/cacm/Friedland67,
  author    = {Paul Friedland},
  title     = {Algorithm 312: Absolute value and square root of a complex
               number},
  journal   = {Commun. ACM},
  volume    = {10},
  number    = {10},
  year      = {1967},
  pages     = {665},
  ee        = {http://doi.acm.org/10.1145/363717.363780},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

 @article{journals/ibmrd/MolerM83,
title = {Replacing Square Roots by Pythagorean Sums.},
author = {Cleve B. Moler and Donald Morrison},
journal = {IBM Journal of Research and Development},
number = {6},
pages = {577-581},
url = {http://dblp.uni-trier.de/db/journals/ibmrd/ibmrd27.html#MolerM83},
volume = {27},
year = {1983},
description = {dblp},
date = {2002-01-03},
keywords = {dblp }
} 

@techreport{900236,
 author = {Lawson,, C. L. and Hanson,, R. J. and Kincaid,, D. R. and Krogh,, F. T.},
 title = {Basic Linear Algebra Subprograms for FORTRAN Usage},
 year = {1977},
 source = {http://www.ncstrl.org:8900/ncstrl/servlet/search?formname=detail\&id=oai%3Ancstrlh%3Autexas_cs%3AUTEXAS_CS%2F%2FCS-TR-77-72},
 publisher = {University of Texas at Austin},
 address = {Austin, TX, USA},
 }

@article{355771,
 author = {Blue,, James L.},
 title = {A Portable Fortran Program to Find the Euclidean Norm of a Vector},
 journal = {ACM Trans. Math. Softw.},
 volume = {4},
 number = {1},
 year = {1978},
 issn = {0098-3500},
 pages = {15--23},
 doi = {http://doi.acm.org/10.1145/355769.355771},
 publisher = {ACM},
 address = {New York, NY, USA},
 }
@InCollection{Cody:1971:SEF,
  author =       "W. J. Cody",
  title =        "Software for the Elementary Functions",
  crossref =     "Rice:1971:MS",
  pages =        "171--186",
  year =         "1971",
  bibdate =      "Thu Sep 15 18:56:47 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt",
  acknowledgement = ack-nj,
}

@techreport{ieee754-1985,
	author = {Stevenson, David  },
	booktitle = {ANSI/IEEE Std 754-1985},
	citeulike-article-id = {1677576},
	journal = {ANSI/IEEE Std 754-1985},
	keywords = {floating-point, para08},
	month = {August},
	posted-at = {2008-04-21 12:47:40},
	priority = {1},
	title = {IEEE standard for binary floating-point arithmetic},
	url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=30711},
	year = {1985}
}

@Book{P754:2008:ISF,
  author =       "{IEEE Task P754}",
  title =        "{IEEE 754-2008, Standard for Floating-Point
                 Arithmetic}",
  publisher =    pub-IEEE-STD,
  address =      pub-IEEE-STD:adr,
  pages =        "58",
  day =          "29",
  month =        aug,
  year =         "2008",
  DOI =          "http://doi.ieeecomputersociety.org/10.1109/IEEESTD.2008.4610935",
  ISBN =         "0-7381-5753-8 (paper), 0-7381-5752-X (electronic)",
  ISBN-13 =      "978-0-7381-5753-5 (paper), 978-0-7381-5752-8
                 (electronic)",
  bibdate =      "Thu Sep 25 09:50:30 2008",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=4610933;
                  http://en.wikipedia.org/wiki/IEEE_754-2008",
  abstract =     "This standard specifies interchange and arithmetic
                 formats and methods for binary and decimal
                 floating-point arithmetic in computer programming
                 environments. This standard specifies exception
                 conditions and their default handling. An
                 implementation of a floating-point system conforming to
                 this standard may be realized entirely in software,
                 entirely in hardware, or in any combination of software
                 and hardware. For operations specified in the normative
                 part of this standard, numerical results and exceptions
                 are uniquely determined by the values of the input
                 data, sequence of operations, and destination formats,
                 all under user control.",
  acknowledgement = ack-nhfb,
}

@article{matlab-hypot,
note={\url{http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/hypot.html&http://www.google.fr/search?q=hypot&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:fr:official&client=firefox-a}},
title={Matlab - hypot : square root of sum of squares},
}

@article{fdlibm,
title = {A Freely Distributable C Math Library},
author = {Sun Microsystems, Inc.},
year = {1993},
note = {\url{http://www.netlib.org/fdlibm}},
}

@book{261217,
 author = {Muller,, Jean-Michel},
 title = {Elementary functions: algorithms and implementation},
 year = {1997},
 isbn = {0-8176-3990-X},
 publisher = {Birkhauser Boston, Inc.},
 address = {Secaucus, NJ, USA},
 }