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@article {Cox84,
author = {David A. Cox},
title = {The arithmetic-geometric mean of {G}auss},
journal = {L'Enseignement Mathématique},
year = {1984},
volume = {30},
number = 2,
pages = {275--330}
}
@phdthesis {Dupont06,
author = {R\'egis Dupont},
title = {Moyenne arithm\'etico-g\'eom\'etrique, suites de
{B}orchardt et applications},
school = {\'Ecole polytechnique},
address = {Palaiseau},
type = {Th\`ese de doctorat},
year = {2006}
}
@Article{Friedland67,
author = {Paul Friedland},
title = {Algorithm 312: {A}bsolute value and square root of a complex
number},
journal = cacm,
year = 1967,
volume = 10,
number = 10,
pages = {665},
annote = "\url{http://portal.acm.org/citation.cfm?id=363780}"
}
@Unpublished{MPFRAlgorithms,
author = {{MPFR Team}},
title = {The {MPFR} {L}ibrary: {A}lgorithms {A}nd {P}roofs},
note = {\url{http://www.mpfr.org/algorithms.pdf}},
}
@Article{Smith98,
author = {David M. Smith},
title = {Algorithm 786: {M}ultiple-Precision Complex Arithmetic and
Functions},
journal = toms,
year = 1998,
volume = 34,
number = 4,
pages = {359--367}
}
@article{CrTh13,
author = {John E. Cremona and Thotsaphon Thongjunthug},
title = {The complex {AGM}, periods of elliptic curves over {$\C$} and complex elliptic logarithms},
journal = "Journal of Number Theory",
volume = 133,
number = 8,
pages = "2813--2841",
year = 2013
}
@Misc{Baudin11,
author = {Michael Baudin},
title = {Error bounds of complex arithmetic},
howpublished = {\url{http://forge.scilab.org/upload/compdiv/files/complexerrorbounds_v0.2.pdf}},
year = 2011}
@Article{Stewart85,
author = {G. W. Stewart},
title = {A Note on Complex Division},
journal = toms,
year = 1985,
volume = 11,
number = 3,
pages = {238--241}}
@Article{Priest04,
author = {Douglas M. Priest},
title = {Efficient Scaling for Complex Division},
journal = toms,
year = 2004,
volume = 30,
number = 4,
pages = {389--401}}
@book{muller:hal-01766584,
TITLE = {{Handbook of Floating-point Arithmetic}},
AUTHOR = {Muller, Jean-Michel and Brunie, Nicolas and de Dinechin, Florent and Jeannerod, Claude-Pierre and Joldes, Mioara and Lef{\`e}vre, Vincent and Melquiond, Guillaume and Revol, Nathalie and Torres, Serge},
URL = {https://hal.inria.fr/hal-01766584},
HAL_LOCAL_REFERENCE = {Rapport LAAS n{\textdegree} 18106},
PUBLISHER = {{Birkh{\"a}user Basel}},
PAGES = {1-627},
YEAR = {2018},
MONTH = Jul,
DOI = {10.1007/978-3-319-76526-6},
KEYWORDS = {arithmetic operators ; arithmetic algorithms ; numerical computing ; floating-point arithmetic ; computer arithmetic},
HAL_ID = {hal-01766584},
HAL_VERSION = {v1},
note = {2nd edition, which contains a chapter on complex numbers}
}
@inproceedings{jeannerod:ensl-01780265,
TITLE = {{On the relative error of computing complex square roots in floating-point arithmetic}},
AUTHOR = {Jeannerod, Claude-Pierre and Muller, Jean-Michel},
URL = {https://hal-ens-lyon.archives-ouvertes.fr/ensl-01780265},
BOOKTITLE = {{ACSSC 2017 - 51st Asilomar Conference on Signals, Systems, and Computers}},
ADDRESS = {Pacific Grove, United States},
PUBLISHER = {{IEEE}},
PAGES = {1-4},
YEAR = {2017},
MONTH = Oct,
DOI = {10.1109/ACSSC.2017.8335442},
PDF = {https://hal-ens-lyon.archives-ouvertes.fr/ensl-01780265/file/asilomar17.pdf},
HAL_ID = {ensl-01780265},
HAL_VERSION = {v1},
}
@Book{AbSt73,
author = "Milton Abramowitz and Irene A. Stegun",
title = "Handbook of Mathematical Functions",
publisher = "Dover",
year = "1973",
note = "\url{http://members.fortunecity.com/aands/toc.htm}"
}
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