Valid HTML 4.0! Valid CSS!
%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.00",
%%%     date            = "15 March 2017",
%%%     time            = "07:57:46 MST",
%%%     filename        = "agm.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "http://www.math.utah.edu/~beebe",
%%%     checksum        = "08521 7855 32347 336149",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "arithmetic--geometric mean; bibliography;
%%%                        BibTeX; geometric--arithmetic mean",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography of publications about
%%%                        the arithmetic--geometric mean (AGM)
%%%                        iteration, discovered by Lagrange before
%%%                        1785, and independently by Carl Friedrich
%%%                        Gauss (1777--1855) in 1799.  Adrien-Marie
%%%                        Legendre (1752--1833) discovered a relation
%%%                        between certain elliptic integrals that led
%%%                        Gauss to apply the AGM to the calculation of
%%%                        the mathematical constant pi.
%%%
%%%                        However, the AGM's first well-known
%%%                        applications, to the high-precision
%%%                        computation of pi, and of high-precision
%%%                        computation of elementary and elliptic
%%%                        functions, were not published until 1971 and
%%%                        1976 (see entries Carlson:1971:AIA,
%%%                        Brent:1976:FMP, and Salamin:1976:CUA).  There
%%%                        was earlier work in the 1920s (see the books
%%%                        and papers by Louis V. King) using the AGM to
%%%                        compute Jacobian elliptic functions, but
%%%                        King's publications seem not to have been
%%%                        widely known or appreciated.
%%%
%%%                        Gauss' work is better known, and the AGM is
%%%                        often (improperly) credited to him alone; see
%%%                        entry Gauss:1992:AGM for a Spanish
%%%                        translation of his original work, from the
%%%                        first publication in the original Latin in
%%%                        his collected works (entry Werke Vol. X-1
%%%                        (1917)).
%%%
%%%                        The AGM provides an iterative process for
%%%                        computing various constants and functions,
%%%                        often with quadratric convergence.  Unlike
%%%                        Newton--Raphson iteration, the AGM process is
%%%                        not self correcting: errors accumulate with
%%%                        each iteration.  That is a disadvantage with
%%%                        hardware arithmetic of fixed precision, but
%%%                        is easily handled in software
%%%                        multiple-precision arithmetic by computing
%%%                        with a few more digits than are eventually
%%%                        needed.  The AGM iteration is comparatively
%%%                        simple to program, and especially for
%%%                        arbitrary-precision arithmetic, provides a
%%%                        convenient way to compute several important
%%%                        constants and functions.
%%%
%%%                        Since the mid-1990s, in a few cases, variants
%%%                        of the AGM have been discovered possessing
%%%                        convergence of order 3, 4, 5, ..., 9.  For
%%%                        example, pi can be calculated to a thousand
%%%                        million digits with only ten 9-th order AGM
%%%                        iterations.
%%%
%%%                        At version 1.00, the year coverage looked
%%%                        like this:
%%%
%%%                             1866 (   1)    1917 (   1)    1968 (   2)
%%%                             1867 (   0)    1918 (   0)    1969 (   1)
%%%                             1868 (   1)    1919 (   0)    1970 (   2)
%%%                             1869 (   0)    1920 (   0)    1971 (   5)
%%%                             1870 (   0)    1921 (   1)    1972 (   3)
%%%                             1873 (   0)    1924 (   1)    1975 (   1)
%%%                             1874 (   0)    1925 (   0)    1976 (   5)
%%%                             1875 (   0)    1926 (   0)    1977 (   1)
%%%                             1876 (   0)    1927 (   0)    1978 (   1)
%%%                             1877 (   0)    1928 (   1)    1979 (   1)
%%%                             1879 (   0)    1930 (   0)    1981 (   3)
%%%                             1881 (   0)    1932 (   0)    1983 (   2)
%%%                             1882 (   0)    1933 (   0)    1984 (   6)
%%%                             1883 (   0)    1934 (   0)    1985 (   2)
%%%                             1884 (   0)    1935 (   0)    1986 (   3)
%%%                             1885 (   0)    1936 (   1)    1987 (   7)
%%%                             1886 (   0)    1937 (   0)    1988 (  19)
%%%                             1887 (   0)    1938 (   0)    1989 (   5)
%%%                             1888 (   0)    1939 (   0)    1990 (   1)
%%%                             1889 (   0)    1940 (   0)    1991 (   5)
%%%                             1890 (   0)    1941 (   0)    1992 (   6)
%%%                             1891 (   0)    1942 (   0)    1993 (  10)
%%%                             1892 (   0)    1943 (   0)    1994 (   8)
%%%                             1893 (   0)    1944 (   0)    1995 (   7)
%%%                             1894 (   0)    1945 (   0)    1996 (  11)
%%%                             1895 (   0)    1946 (   0)    1997 (   9)
%%%                             1896 (   0)    1947 (   0)    1998 (   6)
%%%                             1897 (   0)    1948 (   0)    1999 (   6)
%%%                             1898 (   0)    1949 (   0)    2000 (  10)
%%%                             1899 (   0)    1950 (   0)    2001 (   6)
%%%                             1900 (   0)    1951 (   0)    2002 (   3)
%%%                             1901 (   0)    1952 (   0)    2003 (   8)
%%%                             1902 (   0)    1953 (   0)    2004 (   9)
%%%                             1903 (   0)    1954 (   0)    2005 (   1)
%%%                             1904 (   0)    1955 (   0)    2006 (   6)
%%%                             1905 (   0)    1956 (   2)    2007 (   9)
%%%                             1906 (   0)    1957 (   0)    2008 (   7)
%%%                             1907 (   0)    1958 (   0)    2009 (   6)
%%%                             1908 (   0)    1959 (   0)    2010 (   7)
%%%                             1909 (   0)    1960 (   1)    2011 (   8)
%%%                             1910 (   0)    1961 (   0)    2012 (  10)
%%%                             1911 (   1)    1962 (   0)    2013 (  12)
%%%                             1912 (   0)    1963 (   2)    2014 (   7)
%%%                             1913 (   0)    1964 (   0)    2015 (   9)
%%%                             1914 (   0)    1965 (   2)    2016 (  24)
%%%                             1915 (   0)    1966 (   1)    2017 (   1)
%%%                             1916 (   0)    1967 (   2)
%%%
%%%                             Article:        215
%%%                             Book:            15
%%%                             InCollection:    21
%%%                             InProceedings:   16
%%%                             Misc:             2
%%%                             PhdThesis:        1
%%%                             Proceedings:      6
%%%                             TechReport:       4
%%%                             Unpublished:     19
%%%
%%%                             Total entries:  299
%%%
%%%                        Data for this entry have been collected from
%%%                        the BibNet Project and TeX User Group
%%%                        bibliography archives, and the arXiv.org,
%%%                        Elsevier ScienceDirect, MathSciNet, Springer
%%%                        Link, and Wiley Online databases.
%%%
%%%                        In this bibliography, entries are sorted
%%%                        first by ascending year, and within each
%%%                        year, alphabetically by author or editor,
%%%                        and then, if necessary, by the 3-letter
%%%                        abbreviation at the end of the BibTeX
%%%                        citation tag, using the bibsort -byyear
%%%                        utility.  Year order has been chosen to
%%%                        make it easier to identify the most recent
%%%                        work.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================
@Preamble{
    "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" #
    "\def \cprime {$'$}" #
    "\hyphenation{ }"
}

%%% ====================================================================
%%% Journal abbreviations:
@String{j-ACTA-GEOD-GEOPHYS-HU  = "Acta Geodaetica et Geophysica Hungarica"}

@String{j-AMER-J-PHYSICS        = "American Journal of Physics"}

@String{j-AMER-MATH-MONTHLY     = "American Mathematical Monthly"}

@String{j-ANN-FUNCT-ANAL        = "Annals of Functional Analysis"}

@String{j-ANN-SC-NORM-SUPER-PISA-CL-SCI = "Annali della Scuola normale
                                  superiore di Pisa, Classe di scienze"}

@String{j-APPL-MATH-COMP        = "Applied Mathematics and Computation"}

@String{j-APPL-MATH-MODEL       = "Applied Mathematical Modelling"}

@String{j-APPL-MATH-SCI-RUSE    = "Applied Mathematical Sciences (Ruse)"}

@String{j-ARCH-INEQUAL-APPL     = "Archives of Inequalities and Applications."}

@String{j-C-R-ACAD-SCI-I        = "Comptes rendus de l'Acad{\'e}mie des
                                  sciences. S{\'e}rie I, Math{\'e}matique"}

@String{j-CAN-MATH-BULL         = "Bulletin canadien de
                                  math\-{\'e}\-mat\-iques = Canadian
                                  Mathematical Bulletin"}

@String{j-COMMUN-KOREAN-MATH-SOC = "Communications of the Korean Mathematical
                                  Society"}

@String{j-COMPUT-MATH-APPL      = "Computers and Mathematics with
                                  Applications"}

@String{j-COMPUTERS-AND-GRAPHICS = "Computers and Graphics"}

@String{j-CONST-APPROX          = "Constructive Approximation"}

@String{j-CWI-QUARTERLY         = "CWI Quarterly"}

@String{j-DEUTSCH-MATH-V        = "Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)"}

@String{j-ECON-QUAL-CONTROL     = "Economic Quality Control"}

@String{j-ELEM-MATH             = "Elemente der Mathematik"}

@String{j-ENSEIGN-MATH-2        = "L'Enseignement Math{\'e}matique. Revue
                                  Internationale. 2e S{\'e}rie"}

@String{j-EUR-J-COMB            = "European Journal of Combinatorics"}

@String{j-EXP-MATH              = "Experimental Mathematics"}

@String{j-EXPO-MATH             = "Expositiones Mathematicae"}

@String{j-FIB-QUART             = "Fibonacci Quarterly"}

@String{j-FUNCT-SPACES          = "Journal of Function Spaces"}

@String{j-GAZ-MATH              = "Gazette des Math{\'e}maticiens"}

@String{j-HOKKAIDO-MATH-J       = "Hokkaido Mathematical Journal"}

@String{j-INDIAN-J-MATH         = "Indian Journal of Mathematics"}

@String{j-INT-J-MATH            = "International Journal of Mathematics"}

@String{j-INT-J-MATH-EDU-SCI-TECH = "International Journal of Mathematical
                                  Education in Science and Technology"}

@String{j-INT-J-MATH-MATH-SCI   = "International Journal of Mathematics and
                                  Mathematical Sciences"}

@String{j-INT-J-NUMBER-THEORY   = "International Journal of Number Theory"}

@String{j-INT-J-PROD-ECON       = "International Journal of Production
                                  Economics"}

@String{j-INT-J-SYST-SCI        = "International Journal of Systems Science"}

@String{j-INTERDISCIP-INFORM-SCI = "Interdisciplinary Information Sciences"}

@String{j-IRISH-SOC-BULL        = "Irish Mathematical Society Bulletin"}

@String{j-ISRAEL-J-MATH         = "Israel Journal of Mathematics"}

@String{j-ITAL-J-PURE-APPL-MATH = "Ital. J. Pure Appl. Math."}

@String{j-J-ACM                 = "Journal of the ACM"}

@String{j-J-APPL-MATH           = "Journal of Applied Mathematics"}

@String{j-J-APPROX-THEORY       = "Journal of Approximation Theory"}

@String{j-J-AUTOM-REASON        = "Journal of Automated Reasoning"}

@String{j-J-COMPUT-APPL-MATH    = "Journal of Computational and Applied
                                  Mathematics"}

@String{j-J-ELECTROST           = "Journal of Electrostatics"}

@String{j-J-FUNCT-ANAL          = "Journal of functional analysis"}

@String{j-J-INEQUAL-APPL        = "Journal of Inequalities and Applications"}

@String{j-J-LOND-MATH-SOC       = "Journal of the London Mathematical Society"}

@String{j-J-LOND-MATH-SOC-2     = "Journal of the London Mathematical Society.
                                  Second Series"}

@String{j-J-MATH-ANAL-APPL      = "Journal of Mathematical Analysis and
                                  Applications"}

@String{j-J-MATH-INEQUAL        = "Journal of Mathematical Inequalities"}

@String{j-J-MATH-PHYS           = "Journal of Mathematical Physics"}

@String{j-J-MATH-SCI-ADV-APPL   = "Journal of Mathematical Sciences. Advances
                                  and Applications"}

@String{j-J-NUMBER-THEORY       = "Journal of Number Theory"}

@String{j-JIPAM-J-INEQUAL-PURE-APPL-MATH = "IPAM. Journal of Inequalities in
                                  Pure and Applied Mathematics"}

@String{j-LECT-NOTES-COMP-SCI   = "Lecture Notes in Computer Science"}

@String{j-LECT-NOTES-MATH       = "Lecture Notes in Mathematics"}

@String{j-LIN-MULT-ALGEBRA      = "Linear Multilinear Algebra"}

@String{j-LINEAR-ALGEBRA-APPL   = "Linear Algebra and its Applications"}

@String{j-MAPLE-TECH-NEWS       = "Maple Technical Newsletter"}

@String{j-MATH-ANN              = "Mathematische Annalen"}

@String{j-MATH-COMPUT           = "Mathematics of Computation"}

@String{j-MATH-GAZ              = "The Mathematical Gazette"}

@String{j-MATH-INEQUAL-APPL     = "Mathematical Inequalities \& Applications"}

@String{j-MATH-INTEL            = "The Mathematical Intelligencer"}

@String{j-MATH-MAG              = "Mathematics Magazine"}

@String{j-MATH-PROC-CAMB-PHILOS-SOC = "Mathematical Proceedings of the
                                  Cambridge Philosophical Society"}

@String{j-MATH-STUDENT          = "The Mathematics Student"}

@String{j-NAMS                  = "Notices of the American Mathematical
                                  Society"}

@String{j-NORDISK-MATH-TIDSKR   = "Nordisk Matematisk Tidskrift"}

@String{j-NUM-MATH              = "Numerische Mathematik"}

@String{j-NUMER-FUNCT-ANAL-OPTIM = "Numerical Functional Analysis and
                                  Optimization"}

@String{j-OBZORNIK-MAT-FIZ      = "Obzornik Mat. Fiz."}

@String{j-OCTOGON-MATH-MAG      = "Octogon Mathematical Magazine"}

@String{j-OPER-MATRICES         = "Operators and Matrices"}

@String{j-PAC-J-APPL-MATH       = "Pacific Journal of Applied Mathematics"}

@String{j-PHYS-LET-A            = "Physics Letters A"}

@String{j-PI-MU-EPSILON-J       = "Pi Mu Epsilon Journal"}

@String{j-PROC-AM-MATH-SOC      = "Proceedings of the American Mathematical
                                  Society"}

@String{j-PROC-JAPAN-ACAD-SER-A-MATH-SCI = "Proceedings of the Japan Academy of
                                  Sciences. Series A. Mathematical Sciences"}

@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS = "Proceedings of the Royal Society of
                                  London. Series A, Containing Papers of a
                                  Mathematical and Physical Character"}

@String{j-PUBL-MATH-DEBRECEN    = "Publicationes Mathematicae Debrecen"}

@String{j-RAMANUJAN-J           = "The {Ramanujan} Journal"}

@String{j-REND-CIRC-MAT         = "Rendiconti del Circolo matematico di
                                  Palermo"}

@String{j-RESONANCE             = "Resonance"}

@String{j-SCI-MATH-JPN          = "Scientiae Mathematicae Japonicae"}

@String{j-SIAM-J-APPL-MATH      = "SIAM Journal on Applied Mathematics"}

@String{j-SIAM-J-MAT-ANA-APPL   = "SIAM Journal on Matrix Analysis and
                                  Applications"}

@String{j-SIAM-J-MATH-ANA       = "SIAM Journal on Mathematical Analysis"}

@String{j-SIAM-REVIEW           = "SIAM Review"}

@String{j-STOCH-PROC-APPL       = "Stochastic Processes and Their
                                  Applications"}

@String{j-TAMKANG-J-MATH        = "Tamkang Journal of Mathematics"}

@String{j-TOPOLOGY              = "Topology"}

@String{j-TRANS-AM-MATH-SOC     = "Transactions of the American Mathematical
                                  Society"}

@String{j-Z-ANGE-MATH-MECH      = "{Zeitschrift f{\"u}r Angewandte Mathematik
                                  und Mechanik}"}

@String{j-ZH-VYCHISL-MAT-MAT-FIZ = "Zhurnal Vychislitel'no{u{i}} Matematiki i
                                  Matematichesko{u{i}} Fiziki"}

%%% ====================================================================
%%% Publisher abbreviations:
@String{pub-ACADEMIC            = "Academic Press"}
@String{pub-ACADEMIC:adr        = "New York, NY, USA"}

@String{pub-CAMBRIDGE           = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr       = "Cambridge, UK"}

@String{pub-IEEE                = "IEEE Computer Society Press"}
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300,
                                  Silver Spring, MD 20910, USA"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}

@String{pub-WILEY               = "Wiley"}
@String{pub-WILEY:adr           = "New York, NY, USA"}

%%% ====================================================================
%%% BibTeX entries, sorted by year, and then by citation label:
@Book{Gauss:1866:W,
  author =       "Carl Friedrich Gauss",
  title =        "Werke",
  volume =       "3",
  publisher =    "Koniglichen Gesellschaft der Wissenschaften",
  address =      "G{\"o}ttingen, Germany",
  pages =        "????",
  year =         "1866",
  bibdate =      "Tue Mar 14 19:03:18 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1777--1855",
  remark =       "See pages 361--403 for AGM work.",
}

@InCollection{Lagrange:1868:X,
  author =       "Joseph-Louis Lagrange",
  booktitle =    "{\OE}uvres",
  title =        "????",
  publisher =    "Gauthier-Villars",
  address =      "Paris, France",
  pages =        "253--312",
  year =         "1868",
  bibdate =      "Tue Mar 14 18:45:06 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1736--1813",
  remark =       "See especially pages 267 and 272.",
}

@Article{Schlesinger:1911:GJA,
  author =       "L. Schlesinger",
  title =        "{{\"U}ber Gauss' Jugendarbeiten zum
                 arithmetisch--geometrischen Mittel}. ({German}) [{On}
                 {Gauss}' youthful work on the arithmetic--geometric
                 mean]",
  journal =      j-DEUTSCH-MATH-V,
  volume =       "20",
  number =       "??",
  pages =        "396--403",
  month =        "????",
  year =         "1911",
  bibdate =      "Tue Mar 14 18:38:44 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  ZMnumber =     "42.0466.01",
  acknowledgement = ack-nhfb,
  ajournal =     "Jber. Deutsch. Math.--Verein",
  fjournal =     "Jahresbericht der Deutschen Mathematiker-Vereinigung
                 (DMV)",
  language =     "German",
}

@InCollection{Gauss:1917:OPG,
  author =       "Carl Friedrich Gauss",
  booktitle =    "Werke",
  title =        "De origene propietatibusque generalibus numerorum
                 mediorum aritmet. geometricorum. ({Latin}) []",
  volume =       "X-1",
  publisher =    "Koniglichen Gesellschaft der Wissenschaften",
  address =      "G{\"o}ttingen, Germany",
  pages =        "??--??",
  year =         "1917",
  bibdate =      "Tue Mar 14 17:28:06 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1777--1855",
  language =     "Latin",
  remark =       "This work was not published during Gauss's lifetime
                 (1777--1855).",
}

@Article{King:1921:SNF,
  author =       "Louis Vessot King",
  title =        "On Some New Formulae for the Numerical Calculation of
                 the Mutual Induction of Coaxial Circles",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS,
  volume =       "100",
  number =       "702",
  pages =        "60--66",
  day =          "4",
  month =        oct,
  year =         "1921",
  DOI =          "http://dx.doi.org/10.1098/rspa.1921.0070",
  ISSN =         "0950-1207 (print), 2053-9150 (electronic)",
  bibdate =      "Wed Feb 03 09:07:10 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  note =         "This is the first known publication of the AGM method,
                 discovered by the author in 1913, for computing
                 Jacobian elliptic functions. See also
                 \cite{King:1924:DNC,King:2007:DNC}.",
  URL =          "http://www.jstor.org/stable/93861",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of London. Series A,
                 Containing Papers of a Mathematical and Physical
                 Character",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
}

@Book{King:1924:DNC,
  author =       "Louis Vessot King",
  title =        "On the Direct Numerical Calculation of Elliptic
                 Functions and Integrals",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "viii + 42",
  year =         "1924",
  LCCN =         "QA343",
  bibdate =      "Wed Feb 03 08:53:04 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  remark =       "The AGM method for Jacobian elliptic functions was
                 discovered by this book's author at McGill University
                 in 1913, first published in \cite{King:1921:SNF}, and
                 then in this monograph (reprinted in
                 \cite{King:2007:DNC}).",
}

@Article{Geppert:1928:TAG,
  author =       "Harald Geppert",
  title =        "{Zur Theorie des arithmetisch--geometrischen Mittels}.
                 ({German}) [{On} the theory of the
                 arithmetic--geometric mean]",
  journal =      j-MATH-ANN,
  volume =       "99",
  number =       "1",
  pages =        "162--180",
  month =        dec,
  year =         "1928",
  CODEN =        "MAANA3",
  DOI =          "http://dx.doi.org/10.1007/BF01459092",
  ISSN =         "0025-5831 (print), 1432-1807 (electronic)",
  ISSN-L =       "0025-5831",
  bibdate =      "Tue Mar 14 18:33:51 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01459092",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Annalen",
  journal-URL =  "http://link.springer.com/journal/208",
  language =     "German",
  received =     "04 March 1927",
}

@PhdThesis{Butter:1936:CTA,
  author =       "Franklin A. {Butter, Jr}",
  title =        "A Contribution to the Theory of the
                 Arithmetic--Geometric Mean",
  type =         "Thesis ({Ph.D.})",
  school =       "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  year =         "1936",
  MRclass =      "Thesis",
  MRnumber =     "2937121",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://search.proquest.com/docview/301788817",
  acknowledgement = ack-nhfb,
}

@Article{Bellman:1956:AGM,
  author =       "Richard Bellman",
  title =        "On the arithmetic--geometric mean inequality",
  journal =      j-MATH-STUDENT,
  volume =       "24",
  pages =        "233--234 (1957)",
  year =         "1956",
  CODEN =        "MTHSBH",
  ISSN =         "0025-5742",
  MRclass =      "09.2X",
  MRnumber =     "0085208",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematics Student",
}

@Article{Hunter:1956:GIA,
  author =       "John Hunter",
  title =        "A generalization of the inequality of the
                 arithmetic--geometric means",
  journal =      "Proc. Glasgow Math. Assoc.",
  volume =       "2",
  pages =        "149--158",
  year =         "1956",
  MRclass =      "10.2X",
  MRnumber =     "0075984",
  MRreviewer =   "Harvey Cohn",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Diananda:1960:CNS,
  author =       "P. H. Diananda",
  title =        "Classroom Notes: a Simple Proof of the Arithmetic Mean
                 Geometric Mean Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "67",
  number =       "10",
  pages =        "1007--1007",
  month =        dec,
  year =         "1960",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:36:07 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@Article{Akerberg:1963:CNP,
  author =       "Bengt Akerberg",
  title =        "Classroom Notes: A Proof of the Arithmetic--Geometric
                 Mean Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "70",
  number =       "9",
  pages =        "997--998",
  month =        nov,
  year =         "1963",
  CODEN =        "AMMYAE",
  DOI =          "http://dx.doi.org/10.2307/2313068",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "Contributed Item",
  MRnumber =     "1532378",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Everitt:1963:IGA,
  author =       "W. N. Everitt",
  title =        "On an Inequality for the Generalized Arithmetic and
                 Geometric Means",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "70",
  number =       "3",
  pages =        "251--255",
  month =        mar,
  year =         "1963",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:37:02 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@Book{Pars:1965:TAD,
  author =       "Leopold Alexander Pars",
  title =        "A Treatise on Analytical Dynamics",
  publisher =    "Heinemann",
  address =      "London, UK",
  pages =        "xxi + 641",
  year =         "1965",
  bibdate =      "Wed Mar 15 08:09:52 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Tricomi:1965:SID,
  author =       "F. G. Tricomi",
  title =        "Sull'algoritmo iterativo del {Borchardt} e su di una
                 sua generalizzazione. (Italian) [{On} the iterative
                 algorithm of {Borchardt} and on one of its
                 generalization]",
  journal =      j-REND-CIRC-MAT,
  volume =       "2",
  number =       "14",
  pages =        "85--94",
  month =        "????",
  year =         "1965",
  CODEN =        "RCMMAR",
  ISSN =         "0009-725X (print), 1973-4409 (electronic)",
  ISSN-L =       "0009-725X",
  bibdate =      "Tue Mar 14 18:46:58 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rendiconti del Circolo matematico di Palermo",
}

@TechReport{Tricomi:1966:RUS,
  author =       "F. G. Tricomi",
  title =        "Lectures on the use of special functions by
                 calculations with electronic computers",
  type =         "Lecture Series",
  number =       "47",
  institution =  "The Institute for Fluid Dynamics and Applied
                 Mathematics, University of Maryland, College Park",
  address =      "College Park, MD, USA",
  year =         "1966",
  bibdate =      "Tue Mar 14 18:48:58 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Everitt:1967:LPA,
  author =       "W. N. Everitt",
  title =        "On a limit problem associated with the
                 arithmetic--geometric mean inequality",
  journal =      j-J-LOND-MATH-SOC,
  volume =       "42",
  pages =        "712--718",
  year =         "1967",
  CODEN =        "JLMSAK",
  ISSN =         "0024-6107 (print), 1469-7750 (electronic)",
  ISSN-L =       "0024-6107",
  MRclass =      "26.70",
  MRnumber =     "0222229",
  MRreviewer =   "P. H. Diananda",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "See corrigendum \cite{Everitt:1969:CLP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the London Mathematical Society. Second
                 Series",
  journal-URL =  "http://jlms.oxfordjournals.org/content/by/year",
}

@Article{Gaines:1967:CNA,
  author =       "Fergus Gaines",
  title =        "Classroom Notes: On the Arithmetic Mean--Geometric
                 Mean Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "74",
  number =       "3",
  pages =        "305--306",
  month =        mar,
  year =         "1967",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:38:34 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@Article{OShea:1968:MNA,
  author =       "Siobhan O'Shea",
  title =        "Mathematical Notes: The Arithmetic Geometric Mean
                 Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "75",
  number =       "10",
  pages =        "1092--1093",
  month =        dec,
  year =         "1968",
  CODEN =        "AMMYAE",
  DOI =          "http://dx.doi.org/10.2307/2315738",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "Contributed Item",
  MRnumber =     "1535171",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Book{Pars:1968:TAD,
  author =       "Leopold Alexander Pars",
  title =        "A Treatise on Analytical Dynamics",
  publisher =    "Heinemann",
  address =      "London, UK",
  pages =        "xxi + 641",
  year =         "1968",
  ISBN =         "0-435-52690-1",
  ISBN-13 =      "978-0-435-52690-0",
  bibdate =      "Wed Mar 15 08:09:52 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  remark =       "Reprint of \cite{Pars:1965:TAD} with corrections.",
}

@Article{Everitt:1969:CLP,
  author =       "W. N. Everitt",
  title =        "Corrigendum: {``On a limit problem associated with the
                 arithmetic--geometric mean inequality''}",
  journal =      j-J-LOND-MATH-SOC-2,
  volume =       "1",
  pages =        "428--430",
  year =         "1969",
  CODEN =        "JLMSAK",
  ISSN =         "0024-6107 (print), 1469-7750 (electronic)",
  ISSN-L =       "0024-6107",
  MRclass =      "26.70",
  MRnumber =     "0248309",
  MRreviewer =   "P. H. Diananda",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "See \cite{Everitt:1967:LPA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the London Mathematical Society. Second
                 Series",
  journal-URL =  "http://jlms.oxfordjournals.org/content/by/year",
}

@Article{Carlson:1970:IMA,
  author =       "B. C. Carlson",
  title =        "An Inequality of Mixed Arithmetic and Geometric
                 Means",
  journal =      j-SIAM-REVIEW,
  volume =       "12",
  number =       "2",
  pages =        "287--288",
  month =        "????",
  year =         "1970",
  CODEN =        "SIREAD",
  DOI =          "http://dx.doi.org/10.1137/1012054",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:17 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/12/2;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "April 1970",
}

@Article{Lehmer:1970:CCM,
  author =       "D. H. Lehmer",
  title =        "On the compounding of certain means",
  journal =      j-NAMS,
  volume =       "17",
  number =       "??",
  pages =        "634--635",
  month =        "????",
  year =         "1970",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Tue Mar 14 19:09:32 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  remark =       "Check title: not found in MathSciNet or zbMATH
                 databases, or in Web searches, but cited in \cite[ref.
                 17]{Carlson:1971:AIA}.",
}

@Article{Carlson:1971:AIA,
  author =       "Bille Chandler Carlson",
  title =        "Algorithms Involving Arithmetic and Geometric Means",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "78",
  number =       "5",
  pages =        "496--505",
  month =        may,
  year =         "1971",
  CODEN =        "AMMYAE",
  DOI =          "http://dx.doi.org/10.2307/2317754",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:36:21 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcw.bib; JSTOR
                 database",
  URL =          "http://www.jstor.org/stable/2317754",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Lehmer:1971:CCM,
  author =       "D. H. Lehmer",
  title =        "On the compounding of certain means",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "36",
  number =       "1",
  pages =        "183--200",
  month =        oct,
  year =         "1971",
  CODEN =        "JMANAK",
  DOI =          "http://dx.doi.org/10.1016/0022-247x(71)90029-1",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 18:52:11 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "arithmetic--geometric mean (AGM) iteration; complete
                 elliptic integrals of the first and second kinds.
                 Landen s transformation",
}

@Article{Meany:1971:BRB,
  author =       "R. K. Meany and S. A. Nelson and B. C. Carlson",
  title =        "Book Review: {{\booktitle{An Inequality of Mixed
                 Arithmetic and Geometric Means}} (B. C. Carlson)}",
  journal =      j-SIAM-REVIEW,
  volume =       "13",
  number =       "2",
  pages =        "253--255",
  month =        "????",
  year =         "1971",
  CODEN =        "SIREAD",
  DOI =          "http://dx.doi.org/10.1137/1013058",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:28 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/13/2;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "April 1971",
}

@Article{Morita:1971:CLG,
  author =       "Tohru Morita and Tsuyoshi Horiguchi",
  title =        "Calculation of the lattice {Green}'s function for the
                 bcc, fcc, and rectangular lattices",
  journal =      j-J-MATH-PHYS,
  volume =       "12",
  number =       "6",
  pages =        "986--992",
  month =        jun,
  year =         "1971",
  CODEN =        "JMAPAQ",
  DOI =          "http://dx.doi.org/10.1063/1.1665693",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 16:39:38 MDT 2011",
  bibsource =    "http://jmp.aip.org/;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/jmathphys1970.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v12/i6/p986_s1",
  acknowledgement = ack-nhfb,
  classification = "A0550 (Lattice theory and statistics; Ising
                 problems)",
  corpsource =   "Tohoku Univ., Sendai, Japan",
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  keywords =     "arithmetic mean; bcc lattice; complex modulus;
                 divergence; elliptic integral; fcc lattice; geometric
                 mean; Green's function methods; Lattice Green function;
                 lattice theory and statistics; rectangular lattice",
  onlinedate =   "28 October 2003",
  pagecount =    "7",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Passy:1971:GWM,
  author =       "U. Passy",
  title =        "Generalized Weighted Mean Programming",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "20",
  number =       "4",
  pages =        "763--778",
  month =        jun,
  year =         "1971",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classification = "B0260 (Optimisation techniques); C1180 (Optimisation
                 techniques)",
  corpsource =   "Tech. Israel Inst. Technol., Haifa, Israel",
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  keywords =     "algorithms; arithmetic geometric mean inequality;
                 nonlinear programming; weighted mean programming",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Hering:1972:GAG,
  author =       "Franz Hering",
  title =        "A generalization of the arithmetic--geometric mean
                 inequality and an application to finite sequences of
                 zeros and ones",
  journal =      j-ISRAEL-J-MATH,
  volume =       "11",
  number =       "1",
  pages =        "14--30",
  year =         "1972",
  CODEN =        "ISJMAP",
  DOI =          "http://dx.doi.org/10.1007/BF02761445",
  ISSN =         "0021-2172 (print), 1565-8511 (electronic)",
  ISSN-L =       "0021-2172",
  MRclass =      "05A17",
  MRnumber =     "0302466",
  MRreviewer =   "S. G. Williamson",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02761445",
  acknowledgement = ack-nhfb,
  fjournal =     "Israel Journal of Mathematics",
  journal-URL =  "http://link.springer.com/journal/11856",
}

@Article{Morita:1972:CAG,
  author =       "Tohru Morita and Tsuyoshi Horiguchi",
  title =        "Convergence of the arithmetic--geometric mean
                 procedure for the complex variables and the calculation
                 of the complete elliptic integrals with complex
                 modulus",
  journal =      j-NUM-MATH,
  volume =       "20",
  number =       "5",
  pages =        "425--430",
  month =        oct,
  year =         "1972",
  CODEN =        "NUMMA7",
  DOI =          "http://dx.doi.org/10.1007/BF01402565",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D20",
  MRnumber =     "0315870",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 http://www.math.utah.edu/pub/tex/bib/nummath.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=20&issue=5&spage=425",
  abstract =     "The convergence of the arithmetic--geometric mean
                 procedure is checked for complex variables. The
                 procedure is shown to be useful for the evaluation of
                 the complete elliptic integrals of the first and second
                 kinds with complex modulus. It is suggested that the
                 procedure will be useful also for the numerical
                 calculation of the elliptic integrals and the Jacobian
                 elliptic functions with complex modulus in general.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Thurston:1972:HGU,
  author =       "H. A. Thurston",
  title =        "How good is the usual approximation for the period of
                 a simple pendulum?",
  journal =      j-MATH-GAZ,
  volume =       "56",
  number =       "??",
  pages =        "120--122",
  month =        "????",
  year =         "1972",
  CODEN =        "MAGAAS",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  bibdate =      "Wed Mar 15 07:24:11 2017",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  keywords =     "arithmetic--geometric mean",
}

@Article{Tung:1975:LUB,
  author =       "S. H. Tung",
  title =        "On lower and upper bounds of the difference between
                 the arithmetic and the geometric mean",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "131",
  pages =        "834--836",
  month =        jul,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0240 (Probability and statistics); C1140 (Probability
                 and statistics)",
  corpsource =   "Dept. of Math. and Statistics, Miami Univ., Oxford,
                 OH, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "arithmetic mean; geometric mean; lower bounds;
                 statistics; upper bounds",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Brent:1976:FMP,
  author =       "Richard P. Brent",
  title =        "Fast Multiple-Precision Evaluation of Elementary
                 Functions",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "242--251",
  month =        apr,
  year =         "1976",
  CODEN =        "JACOAH",
  DOI =          "http://dx.doi.org/10.1145/321941.321944",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "68A20 (68A10)",
  MRnumber =     "52 \#16111",
  MRreviewer =   "Amnon Barak",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/jacm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib",
  abstract =     "Let $ f(x) $ be one of the usual elementary functions
                 ($ \exp $, $ \log $, $ \arctan $, $ \sin $, $ \cosh $,
                 etc.), and let $ M(n) $ be the number of
                 single-precision operations required to multiply
                 $n$-bit integers. It is shown that $ f(x) $ can be
                 evaluated, with relative error $ O(2 - n) $, in $
                 O(M(n)l o g (n)) $ operations as $ n \rightarrow \infty
                 $, for any floating-point number $x$ (with an $n$-bit
                 fraction) in a suitable finite interval. From the
                 Sch{\"o}nhage--Strassen bound on $ M(n) $, it follows
                 that an $n$-bit approximation to $ f(x) $ may be
                 evaluated in $ O(n \log_(n) \log \log (n)) $
                 operations. Special cases include the evaluation of
                 constants such as $ \pi^e$, and $ e^\pi $. The
                 algorithms depend on the theory of elliptic integrals,
                 using the arithmetic--geometric mean iteration and
                 ascending Landen transformations.",
  acknowledgement = ack-nhfb,
  classification = "723",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "computational complexity; computer arithmetic;
                 computer programming",
}

@InProceedings{Brent:1976:MPZ,
  author =       "Richard P. Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  crossref =     "Traub:1976:ACC",
  pages =        "151--176",
  year =         "1976",
  MRclass =      "68A20",
  MRnumber =     "54 \#11843",
  MRreviewer =   "Claus-Peter Schnorr",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}

@Article{Fink:1976:GAG,
  author =       "A. M. Fink and Max {Jodeit, Jr.}",
  title =        "A generalization of the arithmetic--geometric means
                 inequality",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "61",
  number =       "2",
  pages =        "255--261 (1977)",
  year =         "1976",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "26A86",
  MRnumber =     "0427564",
  MRreviewer =   "E. F. Beckenbach",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Salamin:1976:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ Using Arithmetic--Geometric
                 Mean",
  journal =      j-MATH-COMPUT,
  volume =       "30",
  number =       "135",
  pages =        "565--570",
  month =        jul,
  year =         "1976",
  CODEN =        "MCMPAF",
  DOI =          "http://dx.doi.org/10.2307/2005327",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "10A30 (10A40 33A25)",
  MRnumber =     "0404124 (53 \#7928)",
  MRreviewer =   "I. John Zucker",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib; JSTOR
                 database; MathSciNet database",
  note =         "See also \cite{Brent:1976:MPZ,Brent:2010:MPZ}.",
  URL =          "http://www.jstor.org/stable/2005327",
  ZMnumber =     "0345.10003",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Charles Stark Draper Lab., Cambridge, MA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "arithmetic geometric mean; convergence; elliptic
                 integrals; error analysis; fast Fourier transform
                 multiplication; function evaluation; Landen's;
                 Legendre's relation; numerical computation of pi;
                 transformation",
  remark =       "Fullerton: A quadratically convergent algorithm.",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Schaumberger:1977:APA,
  author =       "Norman Schaumberger and Bert Kabak",
  title =        "Another proof of the arithmetic--geometric mean
                 inequality",
  journal =      j-PI-MU-EPSILON-J,
  volume =       "6",
  number =       "6",
  pages =        "352--354",
  year =         "1977",
  CODEN =        "PMEJBR",
  ISSN =         "0031-952x",
  MRclass =      "26A86",
  MRnumber =     "0430190",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Pi Mu Epsilon Journal",
}

@Article{Almkvist:1978:AGM,
  author =       "Gert Almkvist",
  title =        "Aritmetisk--geometriska Medelv{\"a}rdet och Ellipsens
                 B{\aa}gl{\"a}ngd. ({Swedish}) [{The}
                 arithmetic--geometric mean and the arc length of the
                 ellipse]",
  journal =      j-NORDISK-MATH-TIDSKR,
  volume =       "25--26",
  number =       "3--4",
  pages =        "121--130, 208",
  year =         "1978",
  ISSN =         "0029-1412, 0801-3500",
  MRclass =      "10D05 (33A25)",
  MRnumber =     "561786",
  MRreviewer =   "Troels J{\o}rgensen",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/24525291",
  acknowledgement = ack-nhfb,
  fjournal =     "Nordisk Matematisk Tidskrift",
  journal-URL =  "http://www.jstor.org/journal/nordmatetids",
  language =     "Swedish",
}

@Book{Pars:1979:TAD,
  author =       "Leopold Alexander Pars",
  title =        "A Treatise on Analytical Dynamics",
  publisher =    "Ox Bow Press",
  address =      "Woodbridge, CT, USA",
  pages =        "xxi + 641",
  year =         "1979",
  ISBN =         "0-918024-07-2",
  ISBN-13 =      "978-0-918024-07-7",
  LCCN =         "QA845 .P32 1979",
  bibdate =      "Wed Mar 15 08:12:22 MDT 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Reprint. Originally published: New York: Wiley,
                 1965.",
  subject =      "Dynamics",
  tableofcontents = "Motion of a particle \\
                 Dynamical Systems \\
                 The first form of the fundamental equation \\
                 The second and third forms of the fundamental equation
                 \\
                 Lagrangian coordinates \\
                 Lagrange's equations \\
                 The theory of rotations \\
                 First applications of Lagrange's equations \\
                 The theory of vibrations \\
                 Further applications of Lagrange's equations \\
                 Variable mass \\
                 The Gibbs--Appell equations \\
                 Applications of the Gibbs--Appell equations \\
                 Impulsive motion \\
                 The sixth form of the fundamental equation \\
                 The Hamilton--Jacobi theorem \\
                 Separable systems with n degrees of freedom \\
                 Systems with one degree of freedom, motion near a
                 singular point \\
                 Systems with one degree of freedom, the cyclic
                 characteristics \\
                 Systems with n degrees of freedom, properties of the
                 characteristics \\
                 Hamilton's equations \\
                 Motion in the neighborhood of a given motion, stability
                 in motion \\
                 Contact transformations \\
                 Transformation theory \\
                 Variation principles \\
                 The principle of Least Action \\
                 The restricted problem of three bodies \\
                 The problem of three bodies \\
                 Periodic orbits",
}

@Article{Cusmariu:1981:MNP,
  author =       "Adolf Cusmariu",
  title =        "Mathematical Notes: a Proof of the Arithmetic
                 Mean--Geometric Mean Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "88",
  number =       "3",
  pages =        "192--194",
  month =        mar,
  year =         "1981",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15 (05A20 40A99)",
  MRnumber =     "82g:26024",
  MRreviewer =   "D. C. Russell",
  bibdate =      "Mon Jun 28 12:36:19 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@Article{Fink:1981:WAG,
  author =       "A. M. Fink",
  title =        "A weighted-arithmetic--geometric means inequality",
  journal =      "Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat.
                 Fiz.",
  number =       "716--734",
  pages =        "35--40",
  year =         "1981",
  ISSN =         "0522-8441",
  MRclass =      "26D15",
  MRnumber =     "642007",
  MRreviewer =   "Peter Bullen",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Univerzitet u Beogradu. Publikacije Elektrotehni\v
                 ckog Fakulteta. Serija Matematika i Fizika",
}

@Article{Heinrich:1981:VAG,
  author =       "H. Heinrich",
  title =        "{Eine Verallgemeinerung des arithmetisch-geometrischen
                 Mittels}. ({German}) [{A} generalization of the
                 arithmetic--geometric mean]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "61",
  number =       "6",
  pages =        "265--267",
  year =         "1981",
  CODEN =        "ZAMMAX",
  DOI =          "http://dx.doi.org/10.1002/zamm.19810610610",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  MRclass =      "26D15",
  MRnumber =     "638023",
  MRreviewer =   "E. F. Beckenbach",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik. Ingenieurwissenschaftliche
                 Forschungsarbeiten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  language =     "German",
}

@Article{Borwein:1983:GAG,
  author =       "D. Borwein and P. B. Borwein",
  title =        "A Generalized Arithmetic--Geometric Mean",
  journal =      j-SIAM-REVIEW,
  volume =       "25",
  number =       "3",
  pages =        "401--401",
  month =        "????",
  year =         "1983",
  CODEN =        "SIREAD",
  DOI =          "http://dx.doi.org/10.1137/1025081",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:53:39 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/25/3;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "July 1983",
}

@Article{Ono:1983:GGT,
  author =       "Takashi Ono",
  title =        "A generalization of {Gauss}' theorem on
                 arithmetic--geometric means",
  journal =      j-PROC-JAPAN-ACAD-SER-A-MATH-SCI,
  volume =       "59",
  number =       "4",
  pages =        "154--157",
  year =         "1983",
  CODEN =        "PJAADT",
  ISSN =         "0386-2194",
  MRclass =      "33A30 (30D10)",
  MRnumber =     "711323",
  MRreviewer =   "R. A. Askey",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://projecteuclid.org/euclid.pja/1195515639",
  acknowledgement = ack-nhfb,
  fjournal =     "Japan Academy. Proceedings. Series A. Mathematical
                 Sciences",
  journal-URL =  "http://projecteuclid.org/pja",
}

@Article{Borwein:1984:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "26",
  number =       "3",
  pages =        "351--366",
  month =        jul,
  year =         "1984",
  CODEN =        "SIREAD",
  DOI =          "http://dx.doi.org/10.1137/1026073",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65D20 (26A09)",
  MRnumber =     "750454; 86d:65029",
  MRreviewer =   "S. Conde",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://epubs.siam.org/toc/siread/26/3;
                 http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://www.jstor.org/stable/2031275",
  abstract =     "We produce a self contained account of the
                 relationship between the Gaussian arithmetic--geometric
                 mean iteration and the fast computation of elementary
                 functions. A particularly pleasant algorithm for pi is
                 one of the by-products.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliationaddress = "Dalhousie Univ, Halifax, NS, Can",
  classification = "723; 921",
  fjournal =     "SIAM Review. A Publication of the Society for
                 Industrial and Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "AGM (Arithmetic--Geometric Mean);
                 arithmetic--geometric mean; calculation of pi;
                 computational methods; elliptic functions; Iterative
                 Methods; mathematical techniques; numerical
                 mathematics",
  onlinedate =   "July 1984",
}

@Article{Borwein:1984:GAG,
  author =       "D. Borwein and P. B. Borwein",
  title =        "A Generalized Arithmetic--Geometric Mean",
  journal =      j-SIAM-REVIEW,
  volume =       "26",
  number =       "3",
  pages =        "433--433",
  month =        jul,
  year =         "1984",
  CODEN =        "SIREAD",
  DOI =          "http://dx.doi.org/10.1137/1026085",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:53:48 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/26/3;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "AGM (Arithmetic--Geometric Mean)",
  onlinedate =   "July 1984",
}

@TechReport{Borwein:1984:RCC,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "Reduced Complexity Calculation of Log",
  number =       "DALTR 84-01",
  institution =  "Department of Mathematics, Dalhousie University",
  address =      "Halifax, NS, Canada",
  pages =        "17",
  month =        jan,
  year =         "1984",
  bibdate =      "Mon Nov 07 17:37:11 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  abstract =     "Various reduced complexity methods for high precision
                 computation of the logarithm are investigated.",
  acknowledgement = ack-nhfb,
  keywords =     "analytic complexity; arithmetic--geometric mean;
                 binary splitting; bit complexity; elliptic integrals;
                 Fast Fourier Transform; logarithms; operational
                 complexity; theta functions",
  remark =       "Typescript, with 84-01 added by hand on cover page.",
}

@Article{Cox:1984:AGM,
  author =       "David A. Cox",
  title =        "The arithmetic--geometric mean of {Gauss}",
  journal =      j-ENSEIGN-MATH-2,
  volume =       "30",
  number =       "3--4",
  pages =        "275--330",
  year =         "1984",
  CODEN =        "ENMAAR",
  ISSN =         "0013-8584 (print), 2309-4672 (electronic)",
  MRclass =      "01A55 (11B83 11F03 14K25)",
  MRnumber =     "767905",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "L'Enseignement Math\'ematique. Revue Internationale.
                 IIe S\'erie",
  journal-URL =  "http://www.e-periodica.ch/digbib/vollist?var=true&UID=ens-001",
}

@Article{Foster:1984:AHM,
  author =       "D. M. E. Foster and G. M. Phillips",
  title =        "The Arithmetic--Harmonic Mean",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "165",
  pages =        "183--191",
  month =        jan,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "40A99 (40A25)",
  MRnumber =     "85j:40008",
  MRreviewer =   "Amnon Jakimovski",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "C1120 (Mathematical analysis)",
  corpsource =   "Maths. Inst., Univ. of St. Andrews, St. Andrews, Fife,
                 UK",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Archimedean process; arithmetic--harmonic; geometric
                 mean; harmonic analysis; harmonic means; mean;
                 sequences",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Schoen:1984:HGA,
  author =       "Robert Schoen",
  title =        "Harmonic, Geometric, and Arithmetic Means in
                 Generalized {Fibonacci} Sequences",
  journal =      j-FIB-QUART,
  volume =       "22",
  number =       "4",
  pages =        "354--357",
  month =        nov,
  year =         "1984",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:00:35 MDT 2011",
  bibsource =    "http://www.fq.math.ca/22-4.html;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/22-4/schoen.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Cox:1985:GAG,
  author =       "David A. Cox",
  title =        "{Gauss} and the arithmetic--geometric mean",
  journal =      j-NAMS,
  volume =       "32",
  number =       "2",
  pages =        "147--151",
  year =         "1985",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  MRclass =      "01A55 (11-03 14-03)",
  MRnumber =     "779224",
  MRreviewer =   "Willard Parker",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
}

@Article{Newman:1985:SVF,
  author =       "D. J. Newman",
  title =        "A simplified version of the fast algorithms of {Brent}
                 and {Salamin}",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "169",
  pages =        "207--210",
  month =        jan,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "86e:65030",
  MRreviewer =   "Walter Gautschi",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "exponential; fast algorithms; function approximation;
                 function approximations; Gauss arithmetic--geometric
                 process; pi",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Borwein:1986:MQC,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "More quadratically converging algorithms for $ \pi $",
  journal =      j-MATH-COMPUT,
  volume =       "46",
  number =       "173",
  pages =        "247--253",
  month =        jan,
  year =         "1986",
  CODEN =        "MCMPAF",
  DOI =          "http://dx.doi.org/10.2307/2008229",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D20",
  MRnumber =     "815846; 87e:65014",
  MRreviewer =   "M. M. Chawla",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib; JSTOR
                 database",
  URL =          "http://docserver.carma.newcastle.edu.au/1614/",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290Z (Other numerical methods); C4130 (Interpolation
                 and function approximation); C4190 (Other numerical
                 methods)",
  corpsource =   "Dalhousie Univ., Halifax, NS, Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "arithmetic--geometric mean iteration; complete
                 elliptic; convergence of numerical methods;
                 Gauss--Legendre iteration; geometry; integrals;
                 iterative; Legendre formula; methods; pi evaluation;
                 quadratically converging algorithms",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Razpet:1986:MAG,
  author =       "Marko Razpet",
  title =        "A method of arithmetic--geometric mean",
  journal =      j-OBZORNIK-MAT-FIZ,
  volume =       "33",
  number =       "6",
  pages =        "161--164",
  year =         "1986",
  CODEN =        "OBMFAY",
  ISSN =         "0473-7446",
  MRclass =      "65D30 (65D32)",
  MRnumber =     "856885",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dru\v stvo Matematikov, Fizikov in Astronomov SRS.
                 Obzornik za Matematiko in Fiziko",
}

@Article{Zulauf:1986:SFE,
  author =       "A. Zulauf",
  title =        "Solution of a functional equation by use of weighted
                 arithmetic--geometric means",
  journal =      j-INDIAN-J-MATH,
  volume =       "28",
  number =       "1",
  pages =        "49--56",
  year =         "1986",
  CODEN =        "IJOMAL",
  ISSN =         "0019-5324",
  MRclass =      "39B40",
  MRnumber =     "868947",
  MRreviewer =   "F. W. Carroll",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Indian Journal of Mathematics",
  journal-URL =  "http://www.amsallahabad.org/ijm.html",
}

@Unpublished{Borwein:1987:AGM,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "15",
  month =        dec,
  year =         "1987",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Canadian Mathematical Society, Coxeter--James Lecture,
                 Vancouver, BC, Canada.",
  acknowledgement = ack-nhfb,
}

@Book{Borwein:1987:PAS,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Pi and the {AGM}: a Study in Analytic Number Theory
                 and Computational Complexity",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xv + 414",
  year =         "1987",
  ISBN =         "0-471-83138-7, 0-471-31515-X (paperback)",
  ISBN-13 =      "978-0-471-83138-9, 978-0-471-31515-5 (paperback)",
  LCCN =         "QA241 .B774 1987",
  MRclass =      "11Y60 (68Q30)",
  MRnumber =     "877728",
  MRreviewer =   "H. London",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Canadian Mathematical Society series of monographs and
                 advanced texts = Monographies et {\'e}tudes de la
                 Soci{\'e}t{\'e} math{\'e}matique du Canada",
  acknowledgement = ack-nhfb,
  remark =       "Chinese edition 1995.",
  subject =      "Number theory; Computational complexity; Elliptic
                 functions; Pi",
  xxURL =        "http://www.loc.gov/catdir/description/wiley032/86015811.html;
                 http://www.loc.gov/catdir/toc/onix02/86015811.html",
}

@Article{Burk:1987:NGL,
  author =       "Frank Burk",
  title =        "Notes: The Geometric, Logarithmic, and Arithmetic Mean
                 Inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "94",
  number =       "6",
  pages =        "527--528",
  month =        jun # "\slash " # jul,
  year =         "1987",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:38:44 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@Article{Cohen:1987:AGM,
  author =       "Joel E. Cohen and Roger D. Nussbaum",
  title =        "Arithmetic--geometric means of positive matrices",
  journal =      j-MATH-PROC-CAMB-PHILOS-SOC,
  volume =       "101",
  number =       "2",
  pages =        "209--219",
  year =         "1987",
  CODEN =        "MPCPCO",
  DOI =          "http://dx.doi.org/10.1017/S0305004100066561",
  ISSN =         "0305-0041 (print), 1469-8064 (electronic)",
  ISSN-L =       "0305-0041",
  MRclass =      "15A51",
  MRnumber =     "870592",
  MRreviewer =   "Ray C. Shiflett",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Proceedings of the Cambridge
                 Philosophical Society",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PSP",
}

@Article{Minassian:1987:AGM,
  author =       "Donald P. Minassian",
  title =        "The arithmetic--geometric mean inequality revisited:
                 elementary calculus and negative numbers",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "94",
  number =       "10",
  pages =        "977--978",
  year =         "1987",
  CODEN =        "AMMYAE",
  DOI =          "http://dx.doi.org/10.2307/2322605",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15",
  MRnumber =     "936057",
  MRreviewer =   "G. A. Heuer",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Minassian:1987:NAG,
  author =       "Donald P. Minassian",
  title =        "Notes: The Arithmetic--Geometric Mean Inequality
                 Revisited: Elementary Calculus and Negative Numbers",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "94",
  number =       "10",
  pages =        "977--978",
  month =        dec,
  year =         "1987",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15",
  MRnumber =     "89e:26035",
  MRreviewer =   "G. A. Heuer",
  bibdate =      "Mon Jun 28 12:38:53 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@Article{Reyssat:1987:AMA,
  author =       "{\'E}ric Reyssat",
  title =        "Approximation des moyennes
                 arithm{\'e}tico--g{\'e}om{\'e}triques. ({French})
                 [{Approximation} of arithmetic--geometric means]",
  journal =      j-ENSEIGN-MATH-2,
  volume =       "33",
  number =       "3--4",
  pages =        "175--181",
  year =         "1987",
  CODEN =        "ENMAAR",
  ISSN =         "0013-8584 (print), 2309-4672 (electronic)",
  MRclass =      "11J82 (11B83 11F11)",
  MRnumber =     "925983",
  MRreviewer =   "John H. Loxton",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "L'Enseignement Math\'ematique. Revue Internationale.
                 IIe S\'erie",
  journal-URL =  "http://www.e-periodica.ch/digbib/vollist?var=true&UID=ens-001",
  language =     "French",
}

@Article{Almkvist:1988:GLR,
  author =       "Gert Almkvist and Bruce Berndt",
  title =        "{Gauss}, {Landen}, {Ramanujan}, the
                 Arithmetic--Geometric Mean, Ellipses, $ \pi $, and the
                 {{\booktitle{Ladies Diary}}}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "95",
  number =       "7",
  pages =        "585--608",
  month =        aug # "\slash " # sep,
  year =         "1988",
  CODEN =        "AMMYAE",
  DOI =          "http://dx.doi.org/10.2307/2323302",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "01A50 (01A55 01A60 33A25)",
  MRnumber =     "966232; 89j:01028",
  MRreviewer =   "R. A. Askey",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib; JSTOR
                 database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Askey:1988:BRP,
  author =       "Richard Askey",
  title =        "Book Review: {{\booktitle{Pi and the AGM}}}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "95",
  number =       "9",
  pages =        "895--897",
  month =        nov,
  year =         "1988",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Sat Aug 13 18:09:13 MDT 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2322925",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  keywords =     "AGM (arithmetic--geometric mean)",
}

@Article{Askey:1988:RPA,
  author =       "Richard Askey",
  title =        "Reviews: {{\em Pi and the AGM}}, by {Jonathan M.
                 Borwein and Peter B. Borwein}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "95",
  number =       "9",
  pages =        "895--897",
  month =        nov,
  year =         "1988",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:39:13 MDT 1999",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
  keywords =     "AGM (arithmetic--geometric mean)",
}

@Article{Berndt:1988:BRJ,
  author =       "Bruce C. Berndt",
  title =        "Book Review: {Jonathan M. Borwein and Peter B.
                 Borwein, \booktitle{Pi and the AGM --- A Study of
                 Analytic Number Theory and Computational Complexity},
                 Canadian Mathematical Society Series of Mono- graphs
                 and Advanced Texts, Wiley, New York, 1987, xv + 414
                 pp., 24 cm. Price \$49.95}",
  journal =      j-MATH-COMPUT,
  volume =       "50",
  number =       "181",
  pages =        "352--354",
  month =        jan,
  year =         "1988",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Sat Aug 13 18:09:13 MDT 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2007942",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Unpublished{Borwein:1988:AGMa,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "13",
  month =        may,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Distinguished Lecturer Series, University of Delaware,
                 Newark, DE, USA.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:1988:AGMb,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "14",
  month =        jun,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, University of Newcastle, Newcastle, NSW,
                 Australia.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:1988:AGMc,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "27",
  month =        jun,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, University of New England, Armidale, NSW,
                 Australia.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:1988:AGMd,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "27",
  month =        jul,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, Auckland University, Auckland, New
                 Zealand.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:1988:AGMe,
  author =       "Jonathan M. Borwein",
  title =        "The arithmetic--geometric mean of {Gauss} and
                 {Legendre}: An Excursion",
  day =          "12",
  month =        sep,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, Macquarie University, Sydney, NSW,
                 Australia.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:1988:BFD,
  author =       "Jonathan M. Borwein",
  title =        "{Borchardt}'s four-dimensional arithmetic--geometric
                 mean",
  day =          "14",
  month =        sep,
  year =         "1988",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Seminar, Macquarie University, Sydney, NSW,
                 Australia.",
  acknowledgement = ack-nhfb,
}

@TechReport{Borwein:1988:CCJ,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "A Cubic Counterpart of {Jacobi}'s Identity and the
                 {AGM}",
  type =         "Report",
  institution =  "Department of Mathematics, Statistics and Computing
                 Science, Dalhousie University",
  address =      "Halifax, NS B3H 3J5, Canada",
  pages =        "20",
  day =          "31",
  month =        dec,
  year =         "1988",
  bibdate =      "Fri Nov 11 07:03:04 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  abstract =     "We produce cubic analogues of Jacobi's celebrated
                 theta function identity and of the
                 arithmetic--geometric mean iteration of Gauss and
                 Legendre. The iteration in question is $ a_{n + 1} =
                 (a_n + 2 b_n) / 3 $ and $ b_{n + 1} = \sqrt
                 [3]{b_n((a_n^2 + a_n b_n + b_n^2) / 3)} $. The limit of
                 this iteration is identified in terms of the
                 hypergeometric function $_2 F_1 (1 / 3, 2 / 3; 1;
                 \cdot)$ which supports a particularly simple cubic
                 transformation.",
  acknowledgement = ack-nhfb,
  keywords =     "$\pi$; arithmetic--geometric mean (AGM); cubic
                 transformations; generalised elliptic functions;
                 hypergeometric functions; mean iterations; theta
                 functions",
}

@Article{Bost:1988:MAG,
  author =       "Jean-Beno{\^{\i}}t Bost and Jean-Fran{\c{c}}ois
                 Mestre",
  title =        "Moyenne arithm{\'e}tico--g{\'e}om{\'e}trique et
                 p{\'e}riodes des courbes de genre $1$ et $2$.
                 ({French}) [{Arithmetic--geometric} mean and periods of
                 the curves of genus $1$ and $2$]",
  journal =      j-GAZ-MATH,
  number =       "38",
  pages =        "36--64",
  year =         "1988",
  ISSN =         "0224-8999",
  MRclass =      "14K20 (11F03 11G05)",
  MRnumber =     "970659",
  MRreviewer =   "Reinhard B{\"o}lling",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Gazette des Math\'ematiciens",
  language =     "French",
}

@Article{Hurley:1988:RCP,
  author =       "Donal Hurley",
  title =        "Recent computations of $ \pi $",
  journal =      j-IRISH-SOC-BULL,
  volume =       "21",
  number =       "??",
  pages =        "38--44",
  year =         "1988",
  ISSN =         "0791-5578",
  MRclass =      "11Y60 (01A50 01A55 01A60 11-03)",
  MRnumber =     "988289 (90e:11194)",
  MRreviewer =   "Kenneth A. Jukes",
  bibdate =      "Mon Apr 25 16:20:53 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Irish Mathematical Society Bulletin",
  journal-URL =  "https://www.maths.tcd.ie/pub/ims/bulletin/",
  keywords =     "agm (arithmetic--geometric mean); Brent--Salamin
                 algorithm (1976); Johann Dase (1824--1861); John Machin
                 (1680--1752)",
  remark =       "No issues before 1995 are available online at
                 http://www.maths.tcd.ie/pub/ims/bulletin/index.php.",
}

@InProceedings{Kanada:1988:VMA,
  author =       "Yasumasa Kanada",
  title =        "Vectorization of multiple-precision arithmetic program
                 and 201,326,000 decimal digits of {$ \pi $}
                 calculation",
  crossref =     "Martin:1988:SPN",
  volume =       "2",
  pages =        "117--128",
  year =         "1988",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib",
  abstract =     "More than 200 million decimal places of {$ \pi $} were
                 calculated using an arithmetic geometric mean formula
                 independently discovered by E. Salamin and R. P. Brent
                 in 1976. Correctness of the calculation was verified
                 through Borwein's quartic convergent formula developed
                 in 1983. The computation took CPU times of 5 hours 57
                 minutes for the main calculation and 7 hours 30 minutes
                 for the verification calculation on the HITAC S-820
                 model 80 supercomputer with 256 MB of main memory and 3
                 GB of high speed semiconductor storage, Extended
                 Storage, to shorten I/O time.\par Computation was
                 completed in 27th of January 1988. At that day two
                 programs generated values up to $ 3 \times 2^{26} $,
                 about 201 million. The two results agreed except for
                 the last 21 digits. These results also agree with the
                 133,554,000 places of calculation of $ \pi $ which was
                 done by the author in January 1987. Compare to the
                 record in 1987, 50\% more decimal digits were
                 calculated with about $ 1 / 6 $ of CPU time.\par
                 Computation was performed with real arithmetic based
                 vectorized Fast Fourier Transform (FFT) multiplier and
                 newly vectorized multiple-precision add, subtract and
                 (single word) constant multiplication programs.
                 Vectorizations for the later cases were realized
                 through first order linear recurrence vector
                 instruction on the S-820. Details of the computation
                 and statistical tests on the first 200 million digits
                 of $ \pi - 3 $ are reported.",
  acknowledgement = ack-nhfb,
  classification = "C4190 (Other numerical methods); C7310
                 (Mathematics)",
  corpsource =   "Comput. Centre, Tokyo Univ., Japan",
  keywords =     "arithmetic geometric mean formula; Borwein's quartic
                 convergent formula; fast Fourier transform; fast
                 Fourier transforms; first order linear recurrence
                 vector instruction; HITAC S-820 model 80 supercomputer;
                 mathematics computing; multiple-precision arithmetic
                 program; multiplier; parallel processing; pi
                 calculation; S-820; vectorization",
  sponsororg =   "IEEE; ACM SIGARCH",
  treatment =    "P Practical",
}

@InProceedings{Kanada:1988:VMP,
  author =       "Yasumasa Kanada",
  booktitle =    "Proceedings of Supercomputing 88. Vol. II: Science and
                 Applications",
  title =        "Vectorization of multiple-precision arithmetic program
                 and 201,326,000 decimal digits of {$ \pi $}
                 calculation",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "117--128",
  year =         "1988",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "http://ieeexplore.ieee.org/;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "More than 200 million decimal places of {\pi} were
                 calculated using an arithmetic geometric mean formula
                 independently discovered by E. Salamin and R. P. Brent
                 in 1976. Correctness of the calculation was verified
                 through Borwein's quartic convergent formula developed
                 in 1983. The computation took CPU times of 5 hours 57
                 minutes for the main calculation and 7 hours 30 minutes
                 for the verification calculation on the HITAC S-820
                 model 80 supercomputer with 256 MB of main memory and 3
                 GB of high speed semiconductor storage, Extended
                 Storage, to shorten I/O time.\par Computation was
                 completed in 27th of January 1988. At that day two
                 programs generated values up to $ 3 \times 2^{26} $,
                 about 201 million. The two results agreed except for
                 the last 21 digits. These results also agree with the
                 133,554,000 places of calculation of $ \pi $ which was
                 done by the author in January 1987. Compare to the
                 record in 1987, 50\% more decimal digits were
                 calculated with about $ 1 / 6 $ of CPU time.\par
                 Computation was performed with real arithmetic based
                 vectorized Fast Fourier Transform (FFT) multiplier and
                 newly vectorized multiple-precision add, subtract and
                 (single word) constant multiplication programs.
                 Vectorizations for the later cases were realized
                 through first order linear recurrence vector
                 instruction on the S-820. Dertails of the computation
                 and statistical tests on the first 200 million digits
                 of $ \pi - 3 $ are reported.",
  acknowledgement = ack-nhfb,
}

@Article{Nishiwada:1988:HSA,
  author =       "Kimimasa Nishiwada",
  title =        "A holomorphic structure of the arithmetic--geometric
                 mean of {Gauss}",
  journal =      j-PROC-JAPAN-ACAD-SER-A-MATH-SCI,
  volume =       "64",
  number =       "9",
  pages =        "322--324",
  year =         "1988",
  CODEN =        "PJAADT",
  ISSN =         "0386-2194",
  MRclass =      "30B99",
  MRnumber =     "979233",
  MRreviewer =   "D. C. Russell",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://projecteuclid.org/euclid.pja/1195513088",
  acknowledgement = ack-nhfb,
  fjournal =     "Japan Academy. Proceedings. Series A. Mathematical
                 Sciences",
  journal-URL =  "http://projecteuclid.org/pja",
}

@Article{Nussbaum:1988:AGM,
  author =       "Roger D. Nussbaum and Joel E. Cohen",
  title =        "The arithmetic--geometric mean and its generalizations
                 for noncommuting linear operators",
  journal =      j-ANN-SC-NORM-SUPER-PISA-CL-SCI,
  volume =       "15",
  number =       "2",
  pages =        "239--308 (1989)",
  year =         "1988",
  CODEN =        "PSNAAI",
  ISSN =         "0391-173x (print), 2036-2145 (electronic)",
  ISSN-L =       "0391-173X",
  MRclass =      "47B15 (26A18 47A60 47H07)",
  MRnumber =     "1007399",
  MRreviewer =   "T. Ando",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.numdam.org/item?id=ASNSP_1988_4_15_2_239_0",
  acknowledgement = ack-nhfb,
  fjournal =     "Annali della Scuola Normale Superiore di Pisa. Classe
                 di Scienze. Serie IV",
}

@Article{Wimp:1988:BRP,
  author =       "Jet Wimp",
  title =        "Book Review: {{\booktitle{Pi and the AGM: a Study in
                 Analytic Number Theory and Computational Complexity}}
                 (Jonathan M. Borwein and Peter B. Borwein)}",
  journal =      j-SIAM-REVIEW,
  volume =       "30",
  number =       "3",
  pages =        "530--533",
  month =        sep,
  year =         "1988",
  CODEN =        "SIREAD",
  DOI =          "http://dx.doi.org/10.1137/1030128",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Aug 13 18:09:13 MDT 2016",
  bibsource =    "http://epubs.siam.org/toc/siread/30/3;
                 http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://www.jstor.org/stable/2030735",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "September 1988",
}

@Article{Borwein:1989:MI,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "On the Mean Iteration $ (a, b) \leftarrow \big (\frac
                 {a + 3b}{4}, \frac {\sqrt {ab} + b}{2} \big) $",
  journal =      j-MATH-COMPUT,
  volume =       "53",
  number =       "187",
  pages =        "311--326",
  month =        jul,
  year =         "1989",
  CODEN =        "MCMPAF",
  DOI =          "http://dx.doi.org/10.2307/2008364",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "30D05 (33A25)",
  MRnumber =     "968148, 90a:30075",
  MRreviewer =   "Carl C. Cowen",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  URL =          "http://docserver.carma.newcastle.edu.au/1586/",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Dept. of Math. Stat. and Comput. Sci., Dalhousie
                 Univ., Halifax, NS, Canada",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computation; convergence of numerical methods;
                 converging process; iterative methods; iterative
                 process; limit; mean iteration; nontrivial
                 identifications; quadratically; symbolic; uniformizing
                 parameters",
  treatment =    "T Theoretical or Mathematical",
}

@Unpublished{Borwein:1989:PAG,
  author =       "Jonathan M. Borwein",
  title =        "Pi and the arithmetic--geometric mean",
  day =          "14",
  month =        apr,
  year =         "1989",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, Rutger's University, New Brunswick, NJ,
                 USA.",
  acknowledgement = ack-nhfb,
}

@Article{Henniart:1989:MAG,
  author =       "Guy Henniart and Jean-Fran{\c{c}}ois Mestre",
  title =        "Moyenne arithm{\'e}tico--g{\'e}om{\'e}trique
                 $p$-adique. ({French}) [$p$-{Adic}
                 arithmetic--geometric mean]",
  journal =      j-C-R-ACAD-SCI-I,
  volume =       "308",
  number =       "13",
  pages =        "391--395",
  year =         "1989",
  CODEN =        "CASMEI",
  ISSN =         "0249-6291",
  ISSN-L =       "0764-4442",
  MRclass =      "11G07 (11F85 11Y99 14G20)",
  MRnumber =     "992515",
  MRreviewer =   "Glenn Stevens",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus des S\'eances de l'Acad\'emie des
                 Sciences. S\'erie I. Math\'ematique",
  language =     "French",
}

@Article{Peetre:1989:GAG,
  author =       "Jaak Peetre",
  title =        "Generalizing the arithmetic geometric mean---a hapless
                 computer experiment",
  journal =      j-INT-J-MATH-MATH-SCI,
  volume =       "12",
  number =       "2",
  pages =        "235--245",
  year =         "1989",
  DOI =          "http://dx.doi.org/10.1155/S016117128900027X",
  ISSN =         "0161-1712 (print), 1687-0425 (electronic)",
  ISSN-L =       "0161-1712",
  MRclass =      "26E99 (01A55 26-03)",
  MRnumber =     "994905",
  MRreviewer =   "Peter Borwein",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
  journal-URL =  "https://www.hindawi.com/journals/ijmms/",
}

@Article{Sala:1989:TJA,
  author =       "Kenneth L. Sala",
  title =        "Transformations of the {Jacobian} amplitude function
                 and its calculation via the arithmetic--geometric
                 mean",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "20",
  number =       "6",
  pages =        "1514--1528",
  month =        nov,
  year =         "1989",
  CODEN =        "SJMAAH",
  DOI =          "http://dx.doi.org/10.1137/0520100",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33A25 (42A16 70D99)",
  MRnumber =     "1019316; 90j:33003",
  MRreviewer =   "J. M. H. Peters",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/20/6;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjmathana.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}

@Article{Nussbaum:1990:CPG,
  author =       "Roger D. Nussbaum and Joel E. Cohen",
  title =        "Convexity properties of generalizations of the
                 arithmetic--geometric mean",
  journal =      j-NUMER-FUNCT-ANAL-OPTIM,
  volume =       "11",
  number =       "1--2",
  pages =        "33--44",
  year =         "1990",
  CODEN =        "NFADOL",
  DOI =          "http://dx.doi.org/10.1080/01630569008816359",
  ISSN =         "0163-0563",
  MRclass =      "26E05 (39B52 46G99 47H99)",
  MRnumber =     "1058775",
  MRreviewer =   "Sever S. Dragomir",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Functional Analysis and Optimization. An
                 International Journal",
  journal-URL =  "http://www.tandfonline.com/loi/lnfa20",
}

@Article{Borwein:1991:CCJ,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "A cubic counterpart of {Jacobi}'s identity and the
                 {AGM}",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "323",
  number =       "2",
  pages =        "691--701",
  month =        feb,
  year =         "1991",
  CODEN =        "TAMTAM",
  DOI =          "http://dx.doi.org/10.2307/2001551",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "33C75 (11F11 11Y60 33C05)",
  MRnumber =     "1010408",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1578/;
                 http://www.jstor.org/stable/2001551",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/tran/",
}

@Article{Bullett:1991:DAG,
  author =       "Shaun Bullett",
  title =        "Dynamics of the arithmetic--geometric mean",
  journal =      j-TOPOLOGY,
  volume =       "30",
  number =       "2",
  pages =        "171--190",
  year =         "1991",
  CODEN =        "TPLGAF",
  DOI =          "http://dx.doi.org/10.1016/0040-9383(91)90004-N",
  ISSN =         "0040-9383 (print), 1879-3215 (electronic)",
  ISSN-L =       "0040-9383",
  MRclass =      "58F08 (58F23)",
  MRnumber =     "1098912",
  MRreviewer =   "Andrew Osbaldestin",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/004093839190004N",
  acknowledgement = ack-nhfb,
  fjournal =     "Topology. An International Journal of Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00409383",
}

@Article{Carlson:1991:IAL,
  author =       "B. C. Carlson and M. Vuorinen",
  title =        "Inequality of the {AGM} and the Logarithmic Mean",
  journal =      j-SIAM-REVIEW,
  volume =       "33",
  number =       "4",
  pages =        "655--655",
  month =        "????",
  year =         "1991",
  CODEN =        "SIREAD",
  DOI =          "http://dx.doi.org/10.1137/1033141",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:54:57 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/33/4;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "December 1991",
}

@Article{Haruki:1991:NCA,
  author =       "Hiroshi Haruki",
  title =        "New characterizations of the arithmetic--geometric
                 mean of {Gauss} and other well-known mean values",
  journal =      j-PUBL-MATH-DEBRECEN,
  volume =       "38",
  number =       "3--4",
  pages =        "323--332",
  year =         "1991",
  CODEN =        "PUMAAR",
  ISSN =         "0033-3883 (print), 2064-2849 (electronic)",
  MRclass =      "39B22 (26D99)",
  MRnumber =     "1113240",
  MRreviewer =   "Zsolt P{\'a}les",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Publicationes Mathematicae Debrecen",
  journal-URL =  "http://publi.math.unideb.hu/",
}

@Article{Szyszkowicz:1991:PGL,
  author =       "Mieczyslaw Szyszkowicz",
  title =        "Patterns generated by logical operators",
  journal =      j-COMPUTERS-AND-GRAPHICS,
  volume =       "15",
  number =       "2",
  pages =        "299--300",
  year =         "1991",
  CODEN =        "COGRD2",
  ISSN =         "0097-8493 (print), 1873-7684 (electronic)",
  ISSN-L =       "0097-8493",
  bibdate =      "Fri Feb 07 10:57:32 1997",
  bibsource =    "Compendex database; Graphics/imager/imager.91.bib;
                 Graphics/siggraph/91.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/compgraph.bib",
  acknowledgement = ack-nhfb,
  classification = "723; 921",
  fjournal =     "Computers \& Graphics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00978493",
  journalabr =   "Comput Graphics (Pergamon)",
  keywords =     "Aesthetic Patterns; Arithmetic Geometric Mean
                 Iterations; Computer Graphics; Computer Metatheory ---
                 Formal Logic; Logical Operators; Mathematical
                 Techniques --- Iterative Methods; Research",
}

@Article{Braden:1992:IAL,
  author =       "B. Braden and B. Danloy and F. Schmidt",
  title =        "Inequality of the {AGM} and the Logarithmic Mean",
  journal =      j-SIAM-REVIEW,
  volume =       "34",
  number =       "4",
  pages =        "653--654",
  month =        "????",
  year =         "1992",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "December 1992",
}

@Article{Cohen:1992:RAG,
  author =       "Joel E. Cohen and Thomas M. Liggett",
  title =        "Random arithmetic--geometric means and random pi:
                 observations and conjectures",
  journal =      j-STOCH-PROC-APPL,
  volume =       "41",
  number =       "2",
  pages =        "261--271",
  year =         "1992",
  CODEN =        "STOPB7",
  DOI =          "http://dx.doi.org/10.1016/0304-4149(92)90126-B",
  ISSN =         "0304-4149 (print), 1879-209x (electronic)",
  ISSN-L =       "0304-4149",
  MRclass =      "60J05 (65D20 65U05)",
  MRnumber =     "1164179",
  MRreviewer =   "M. Iosifescu",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/030441499290126B",
  abstract =     "Two random versions of the arithmetic--geometric mean
                 of Gauss, Lagrange and Legendre are defined. Almost
                 sure convergence and nondegeneracy are proved. These
                 random arithmetic--geometric means in turn define two
                 random versions of $ \pi $. Based on numerical
                 simulations, inequalities and equalities are
                 conjectured. A special case is proved. Further proofs
                 are invited.",
  acknowledgement = ack-nhfb,
  fjournal =     "Stochastic Processes and Their Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03044149",
  keywords =     "elliptic integrals; Markov processes with discrete
                 parameter; nonlinear iteration; pi",
}

@Unpublished{Dijkstra:1992:AMG,
  author =       "Edsger W. Dijkstra",
  title =        "The arithmetic mean and the geometric mean",
  month =        oct,
  year =         "1992",
  bibdate =      "Mon Mar 16 08:14:00 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Circulated privately.",
  URL =          "http://www.cs.utexas.edu/users/EWD/ewd11xx/EWD1140.PDF",
  acknowledgement = ack-nhfb,
  filesize =     "75 KB",
  oldlabel =     "EWD:EWD1140",
}

@Article{Gauss:1992:AGM,
  author =       "Karl F. Gauss",
  title =        "La media aritm{\'e}tico geom{\'e}trica [The
                 arithmetic--geometric mean] (de origene propietati
                 busque generalis numerorum mediorum
                 aritmeticorum-geometricorum)",
  journal =      "Bol. Mat.",
  volume =       "23",
  number =       "1--2",
  pages =        "69--79",
  year =         "1992",
  CODEN =        "BOMAD4",
  ISSN =         "0120-0380 (print), 2357-6529 (electronic)",
  ISSN-L =       "0120-0380",
  MRclass =      "01A75 (01A55)",
  MRnumber =     "1221411",
  MRreviewer =   "Thomas Archibald",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Translated from the Latin original by Fabio Hernando
                 Ortiz.",
  URL =          "http://revistas.unal.edu.co/index.php/bolma/article/view/18204",
  acknowledgement = ack-nhfb,
  author-dates = "1777--1855",
  fjournal =     "Bolet{\'\i}n de Matem{\'a}ticas",
  remark =       "The Math Reviews commentary on this article reports
                 some deficiencies and omissions in the translation, and
                 notes that Gauss' Latin title was ``de origene
                 propietatibusque generalibus numerorum mediorum
                 aritmet. geometricorum''.",
}

@Article{Kittaneh:1992:NAG,
  author =       "Fuad Kittaneh",
  title =        "A note on the arithmetic--geometric-mean inequality
                 for matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "171",
  pages =        "1--8",
  year =         "1992",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/0024-3795(92)90247-8",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A42",
  MRnumber =     "1165442",
  MRreviewer =   "Shao Kuan Li",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Todd:1992:BRB,
  author =       "John Todd and Bill Braden and Bernard Danloy and Frank
                 Schmidt",
  title =        "Book Review: {{\booktitle{Inequality of the AGM and
                 the Logarithmic Mean}} (B. C. Carlson and M.
                 Vuorinen)}",
  journal =      j-SIAM-REVIEW,
  volume =       "34",
  number =       "4",
  pages =        "653--654",
  month =        "????",
  year =         "1992",
  CODEN =        "SIREAD",
  DOI =          "http://dx.doi.org/10.1137/1034127",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:55:07 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/34/4;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "December 1992",
}

@Article{Bencze:1993:NPAa,
  author =       "Mihaly Bencze and Norman Schaumberger",
  title =        "A New Proof of the Arithmetic--Geometric Mean
                 Inequality",
  journal =      j-MATH-MAG,
  volume =       "66",
  number =       "4",
  pages =        "245",
  year =         "1993",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  MRclass =      "Contributed Item",
  MRnumber =     "1572972",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2690740?origin=pubexport",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@Article{Bencze:1993:NPAb,
  author =       "M. Bencze",
  title =        "A new proof of the arithmetic--geometric mean
                 inequality",
  journal =      j-OCTOGON-MATH-MAG,
  volume =       "1",
  number =       "1",
  pages =        "9--10",
  year =         "1993",
  ISSN =         "1222-5657 (print), 2248-1893 (electronic)",
  MRclass =      "26-01 (26D20 40A99)",
  MRnumber =     "1270849",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Octogon Mathematical Magazine",
}

@Article{Bhatia:1993:MMF,
  author =       "Rajendra Bhatia and Chandler Davis",
  title =        "More Matrix Forms of the Arithmetic--Geometric Mean
                 Inequality",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "14",
  number =       "1",
  pages =        "132--136",
  month =        jan,
  year =         "1993",
  CODEN =        "SJMAEL",
  DOI =          "http://dx.doi.org/10.1137/0614012",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A45 (15A60 47A63)",
  MRnumber =     "1199551; 94b:15017",
  MRreviewer =   "Ching-Tsuan Pan",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Borwein:1993:HAA,
  author =       "J. Borwein and P. Borwein and F. Garvan",
  title =        "Hypergeometric analogues of the arithmetic--geometric
                 mean iteration",
  journal =      j-CONST-APPROX,
  volume =       "9",
  number =       "4",
  pages =        "509--523",
  year =         "1993",
  DOI =          "http://dx.doi.org/10.1007/BF01204654",
  ISSN =         "0176-4276 (print), 1432-0940 (electronic)",
  ISSN-L =       "0176-4276",
  MRclass =      "33C05",
  MRnumber =     "1237931",
  MRreviewer =   "Bruce C. Berndt",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1556/;
                 http://link.springer.com/article/10.1007/BF01204654",
  acknowledgement = ack-nhfb,
  fjournal =     "Constructive Approximation. An International Journal
                 for Approximations and Expansions",
  journal-URL =  "http://link.springer.com/journal/365",
}

@Article{Borwein:1993:ICM,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Inequalities for Compound Mean Iterations with
                 Logarithmic Asymptotes",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "177",
  number =       "2",
  pages =        "572--582",
  year =         "1993",
  CODEN =        "JMANAK",
  DOI =          "http://dx.doi.org/10.1006/jmaa.1993.1278",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "33B99",
  MRnumber =     "1231502",
  MRreviewer =   "P. Anandani",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1553/;
                 http://www.sciencedirect.com/science/article/pii/S0022247X83712783",
  abstract =     "We consider the compound means arising as limits from
                 the arithmetic--geometric mean iteration and related
                 iterations. Each of these iterations possesses a
                 logarithmic asymptote. We show that these limit means
                 satisfy very precise inequalities. These can be deduced
                 in a quite uniform fashion from a `comparison lemma'
                 for compound means.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@Article{Bullett:1993:RSP,
  author =       "Shaun Bullett and Jaroslav Stark",
  title =        "Renormalizing the Simple Pendulum",
  journal =      j-SIAM-REVIEW,
  volume =       "35",
  number =       "4",
  pages =        "631--640",
  month =        dec,
  year =         "1993",
  CODEN =        "SIREAD",
  DOI =          "http://dx.doi.org/10.1137/1035140",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "70-01 (33E05 70K99)",
  MRnumber =     "94i:70001",
  MRreviewer =   "Coraci P. Malta",
  bibdate =      "Sat Mar 29 09:55:16 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/35/4;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  abstract =     "The authors present an elementary scheme for
                 calculating the period of oscillation or rotation of a
                 simple pendulum. It is based on the invariance of the
                 complete elliptic integral of the first kind under the
                 arithmetic--geometric mean iteration. They explain how
                 this scheme can be interpreted as an example of
                 renormalization, a technique with many recent
                 applications in both physics and applied mathematics.",
  acknowledgement = ack-nhfb,
  affiliation =  "Queen Mary and Westfield Coll",
  affiliationaddress = "London, Engl",
  classification = "921.2; 921.3; 921.6; 931.1; 943.1",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "Algorithms; Arithmetic--geometric mean; Elliptic
                 integral; Equations of motion; Hamiltonian formalism;
                 Integration; Iterative methods; Landen's
                 transformation; Mathematical transformations;
                 Oscillations; Pendulums; Renormalization; Rotation",
  onlinedate =   "December 1993",
}

@Article{Hao:1993:RAG,
  author =       "Zhi Chuan Hao",
  title =        "A refinement of the arithmetic--geometric means
                 inequality",
  journal =      "J. Math. Res. Exposition",
  volume =       "13",
  number =       "1",
  pages =        "84--88",
  year =         "1993",
  CODEN =        "SYPIET",
  ISSN =         "1000-341X",
  MRclass =      "26D15 (26D05)",
  MRnumber =     "1211057",
  MRreviewer =   "Hiroshi Haruki",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Research and Exposition",
}

@InCollection{Karmer:1993:MPC,
  author =       "W. Karmer",
  title =        "Multiple-precision computations with result
                 verification",
  crossref =     "Adams:1993:SCA",
  pages =        "325--356",
  month =        "????",
  year =         "1993",
  bibdate =      "Thu Dec 14 17:22:42 MST 1995",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  abstract =     "Multiple-precision real and interval modules for
                 PASCAL-XSC have been developed. These modules are used
                 to illustrate a variety of algorithms for the following
                 purposes: multiple-precision evaluation of the function
                 square root with maximum accuracy, the
                 arithmetic--geometric mean iteration, different methods
                 for the computation of a large number of digits of pi,
                 the computation of elliptic integrals, the computation
                 of guaranteed bounds for the natural logarithm, and the
                 computation of e/sup pi / using a representation of
                 this value by an infinite product. In general,
                 enclosures for the desired values are computed. Due to
                 the concept of overloading of functions and the
                 operator concept of PASCAL-XSC the programs become
                 clear and readable.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe Univ., Germany",
  classification = "C5230 (Digital arithmetic methods); C6140D (High
                 level languages); C7310 (Mathematics)",
  keywords =     "Arithmetic--geometric mean iteration; Elliptic
                 integrals; Enclosures; Function square root; Guaranteed
                 bounds; Infinite product; Interval modules; Maximum
                 accuracy; Multiple-precision evaluation; Natural
                 logarithm; Operator concept; PASCAL-XSC; Result
                 verification",
  pageswhole =   "x + 612",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; High level languages; Mathematics
                 computing; Pascal",
}

@InCollection{Kramer:1993:MPC,
  author =       "Walter Kr{\"a}mer",
  booktitle =    "Mathematics in Science and Engineering: Scientific
                 Computing with Automatic Result Verification",
  title =        "Multiple-Precision Computations with Result
                 Verification",
  volume =       "189",
  publisher =    "Elsevier BV",
  address =      "Amsterdam, The Netherlands",
  pages =        "325--356",
  year =         "1993",
  DOI =          "http://dx.doi.org/10.1016/s0076-5392(08)62851-9",
  bibdate =      "Tue Mar 14 19:20:47 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic-geometric mean iteration; computation of $
                 e^\pi $; computation of a large number of digits of
                 $\pi$; computation of elliptic integrals; computation
                 of guaranteed bounds for the natural logarithm;
                 interval arithmetic; PASCAL-XSC",
}

@Article{Bencze:1994:NPW,
  author =       "M. Bencze",
  title =        "A new proof of the weighted arithmetic--geometric mean
                 inequality",
  journal =      j-OCTOGON-MATH-MAG,
  volume =       "2",
  number =       "1",
  pages =        "17--18",
  year =         "1994",
  ISSN =         "1222-5657 (print), 2248-1893 (electronic)",
  MRclass =      "26D20",
  MRnumber =     "1303995",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Octogon Mathematical Magazine",
}

@Unpublished{Dijkstra:1994:AAA,
  author =       "Edsger W. Dijkstra",
  title =        "The argument about the arithmetic mean and the
                 geometric mean, heuristics included",
  month =        jan,
  year =         "1994",
  bibdate =      "Mon Mar 16 08:14:00 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Circulated privately.",
  URL =          "http://www.cs.utexas.edu/users/EWD/ewd11xx/EWD1171.PDF",
  acknowledgement = ack-nhfb,
  filesize =     "137 KB",
  oldlabel =     "EWD:EWD1171",
}

@Article{Dzhaparidze:1994:SAI,
  author =       "Kacha Dzhaparidze and Ren{\'e} H. P. Janssen",
  title =        "A stochastic approach to an interpolation problem with
                 applications to {Hellinger} integrals and
                 arithmetic--geometric mean relationship",
  journal =      j-CWI-QUARTERLY,
  volume =       "7",
  number =       "3",
  pages =        "245--258",
  year =         "1994",
  ISSN =         "0922-5366",
  MRclass =      "41A05 (41A55)",
  MRnumber =     "1328044",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Centrum voor Wiskunde en Informatica. Centre for
                 Mathematics and Computer Science. CWI Quarterly",
}

@Article{Furuta:1994:NAG,
  author =       "Takayuki Furuta",
  title =        "A note on the arithmetic--geometric mean inequality
                 for every unitarily invariant matrix norm",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "208--209",
  number =       "??",
  pages =        "223--228",
  year =         "1994",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/0024-3795(94)90439-1",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A60",
  MRnumber =     "1287348; 95f:15020",
  MRreviewer =   "Frank Hansen",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0024379594904391",
  abstract =     "We integrate ten unitarily invariant matrix norm
                 inequalities equivalent to the Heinz inequality.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
}

@InCollection{Garvan:1994:CMI,
  author =       "Frank Garvan",
  booktitle =    "The {Rademacher} legacy to mathematics ({University}
                 {Park}, {PA}, 1992)",
  title =        "Cubic modular identities of {Ramanujan},
                 hypergeometric functions and analogues of the
                 arithmetic--geometric mean iteration",
  volume =       "166",
  publisher =    "Amer. Math. Soc., Providence, RI",
  pages =        "245--264",
  year =         "1994",
  DOI =          "http://dx.doi.org/10.1090/conm/166/01633",
  MRclass =      "39B12 (11F11 33C55)",
  MRnumber =     "1284065",
  MRreviewer =   "R. A. Askey",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Contemp. Math.",
  acknowledgement = ack-nhfb,
}

@Article{Kittaneh:1994:SOI,
  author =       "Fuad Kittaneh",
  title =        "On some operator inequalities",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "208--209",
  number =       "??",
  pages =        "19--28",
  year =         "1994",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/0024-3795(94)90427-8",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0024379594904278",
  abstract =     "For Hilbert-space operators $S$, $T$ with $S$
                 invertible and self-adjoint, Corach, Porta, and Recht
                 recently proved that $ || S T S^{-1} + S^{-1} T S ||
                 \geq 2 || T ||$. A generalization of this inequality to
                 larger classes of operators and norms is obtained as an
                 immediate consequence of the operator form of the
                 arithmetic--geometric-mean inequality. Some related
                 inequalities are also discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Nishiwada:1994:HSA,
  author =       "Kimimasa Nishiwada",
  title =        "Holomorphic structure of the arithmetic--geometric
                 mean of {Gauss}. {II}",
  journal =      j-PROC-JAPAN-ACAD-SER-A-MATH-SCI,
  volume =       "70",
  number =       "5",
  pages =        "119--122",
  year =         "1994",
  CODEN =        "PJAADT",
  ISSN =         "0386-2194",
  MRclass =      "30B99 (40A05)",
  MRnumber =     "1291164",
  MRreviewer =   "D. C. Russell",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://projecteuclid.org/euclid.pja/1195511045",
  acknowledgement = ack-nhfb,
  fjournal =     "Japan Academy. Proceedings. Series A. Mathematical
                 Sciences",
  journal-URL =  "http://projecteuclid.org/pja",
}

@Article{Vamanamurthy:1994:IM,
  author =       "M. K. Vamanamurthy and M. Vuorinen",
  title =        "Inequalities for Means",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "183",
  number =       "1",
  pages =        "155--166",
  year =         "1994",
  CODEN =        "JMANAK",
  DOI =          "http://dx.doi.org/10.1006/jmaa.1994.1137",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X84711371",
  abstract =     "A monotone form of L'Hospital's rule is obtained and
                 applied to derive inequalities between the
                 arithmetic--geometric mean of Gauss, the logarithmic
                 mean, and Stolarsky's identric mean. Some related
                 inequalities are given for complete elliptic
                 integrals.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@Unpublished{Borwein:1995:CAD,
  author =       "Jonathan M. Borwein",
  title =        "The cubic {AGM} discovered",
  day =          "26",
  month =        oct,
  year =         "1995",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Specialist Colloquium Lecture, University of Utrecht,
                 Utrecht, The Netherlands.",
  acknowledgement = ack-nhfb,
}

@Article{Feng:1995:RAG,
  author =       "Ci Huang Feng",
  title =        "A refinement of the arithmetic--geometric mean
                 inequality",
  journal =      "J. Hangzhou Univ. Natur. Sci. Ed.",
  volume =       "22",
  number =       "3",
  pages =        "222--225",
  year =         "1995",
  CODEN =        "HHHPD7",
  ISSN =         "0253-3618",
  MRclass =      "26D15",
  MRnumber =     "1359614",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Hangzhou University. Natural Science
                 Edition. Hangzhou Daxue Xuebao. Ziran Kexue Ban",
}

@Article{Horn:1995:NBH,
  author =       "Roger A. Horn",
  title =        "Norm Bounds for {Hadamard} Products and an
                 Arithmetic--Geometric Mean Inequality for Unitarily
                 Invariant Norms",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "223--224",
  number =       "1--3",
  pages =        "355--361",
  day =          "??",
  month =        jul,
  year =         "1995",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/0024-3795(94)00034-B",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A45 (15A60 47A63)",
  MRnumber =     "1340700; 96h:15020",
  MRreviewer =   "Roy Mathias",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala1990.bib",
  note =         "Special issue honoring Miroslav Fiedler and Vlastimil
                 Pt{\'a}k.",
  URL =          "http://www.sciencedirect.com/science/article/pii/002437959400034B",
  abstract =     "An arithmetic--geometric mean inequality for unitarily
                 invariant norms and matrices, $ 2 || A \star X B ||
                 \leq || A A \star X + X B B \star || $, is an immediate
                 consequence of a basic inequality for singular values
                 of Hadamard products.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
}

@Article{Lucht:1995:AGM,
  author =       "Lutz G. Lucht",
  title =        "On the arithmetic--geometric mean inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "102",
  number =       "8",
  pages =        "739--740",
  month =        oct,
  year =         "1995",
  CODEN =        "AMMYAE",
  DOI =          "http://dx.doi.org/10.2307/2974645",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15",
  MRnumber =     "1 357 492",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Matsuda:1995:IPM,
  author =       "Takashi Matsuda",
  title =        "An inductive proof of a mixed arithmetic--geometric
                 mean inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "102",
  number =       "7",
  pages =        "634--637",
  month =        aug # "\slash " # sep,
  year =         "1995",
  CODEN =        "AMMYAE",
  DOI =          "http://dx.doi.org/10.2307/2974561",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15",
  MRnumber =     "1349877; 96h:26021",
  MRreviewer =   "Zsolt P{\'a}les",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@InProceedings{Sole:1995:A,
  author =       "Patrick Sole",
  title =        "{$ D_4 $}, {$ E_6 $}, {$ E_8 $} and the {AGM}",
  crossref =     "Cohen:1995:AAA",
  volume =       "948",
  pages =        "448--455",
  year =         "1995",
  CODEN =        "LNCSD9",
  DOI =          "http://dx.doi.org/10.1007/3-540-60114-7_35",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Mar 14 15:36:33 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/lncs1995a.bib",
  abstract =     "We derive Jacobi's quartic identity and the Borweins'
                 cubic identity related to Ramanujan's quadratic modular
                 equation on theta series by lattice enumerative
                 methods. Both identities are instrumental in recent
                 work of the Borweins on the Arithmetic Geometric Mean.
                 Of great use are the constructions of the root lattices
                 $ D_4 $ and $ E_6 $ by binary and ternary codes
                 respectively. A third identity, equally due to the
                 Borweins is also derived in relation to the root
                 lattice $ E_8 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Alzer:1996:PAM,
  author =       "Horst Alzer",
  title =        "A proof of the arithmetic mean-geometric mean
                 inequality",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "103",
  number =       "7",
  pages =        "585--585",
  month =        aug # "\slash " # sep,
  year =         "1996",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26D15",
  MRnumber =     "1 404 083",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/page/journal/amermathmont/about.html",
}

@InProceedings{Dijkstra:1996:AAA,
  author =       "Edsger W. Dijkstra",
  title =        "The argument about the arithmetic mean and the
                 geometric mean, heuristics included",
  crossref =     "Broy:1996:DPD",
  pages =        "29--32",
  year =         "1996",
  bibdate =      "Wed Mar 18 12:28:57 2015",
  bibsource =    "DBLP;
                 http://dblp.uni-trier.de/db/conf/nato/dpd1996.html#Dijkstra96g;
                 http://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 http://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/DBLP/1996.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Unpublished{Dijkstra:1996:AGM,
  author =       "Edsger W. Dijkstra",
  title =        "The arithmetic and geometric means once more",
  month =        feb,
  year =         "1996",
  bibdate =      "Mon Mar 16 08:14:00 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Circulated privately.",
  URL =          "http://www.cs.utexas.edu/users/EWD/ewd12xx/EWD1231.PDF",
  acknowledgement = ack-nhfb,
  filesize =     "63 KB",
  oldlabel =     "EWD:EWD1231",
}

@Article{Kaufmann:1996:IBM,
  author =       "Matt Kaufmann and Paolo Pecchiari",
  title =        "Interaction with the {Boyer--Moore} theorem prover: A
                 tutorial study using the arithmetic--geometric mean
                 theorem",
  journal =      j-J-AUTOM-REASON,
  volume =       "16",
  number =       "1--2",
  pages =        "181--222",
  month =        mar,
  year =         "1996",
  CODEN =        "JAREEW",
  DOI =          "http://dx.doi.org/10.1007/BF00244463",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  MRclass =      "68T15 (03B35)",
  MRnumber =     "1390909",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00244463",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
}

@InProceedings{Kaufmann:1996:IBT,
  author =       "Matt Kaufmann and Paolo Pecchiari",
  title =        "Interaction with the {Boyer--Moore} Theorem Prover: a
                 Tutorial Study Using the Arithmetic--Geometric Mean
                 Theorem",
  crossref =     "Zhang:1996:AMI",
  pages =        "181--222",
  year =         "1996",
  DOI =          "http://dx.doi.org/10.1007/978-94-009-1675-3_6",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-94-009-1675-3_6",
  acknowledgement = ack-nhfb,
  remark =       "This chapter presents a formal proof with the Boyer
                 -Moore Theorem Prover that the arithmetic mean of a
                 sequence of natural numbers is greater than or equal to
                 their geometric mean.",
}

@InProceedings{Luther:1996:CAG,
  author =       "Wolfram Luther and Werner Otten",
  title =        "The Complex Arithmetic--Geometric Mean and
                 Multiple-Precision Matrix Functions",
  crossref =     "Alefeld:1996:SCV",
  pages =        "52--58",
  year =         "1996",
  MRclass =      "65G10 (65H99)",
  MRnumber =     "1394225",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Neuman:1996:TIA,
  author =       "Edward Neuman",
  title =        "Three Inequalities for the Arithmetic, Identric, and
                 Geometric Means",
  journal =      j-SIAM-REVIEW,
  volume =       "38",
  number =       "2",
  pages =        "315--315",
  month =        "????",
  year =         "1996",
  CODEN =        "SIREAD",
  DOI =          "http://dx.doi.org/10.1137/1038050",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:55:40 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/38/2;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "June 1996",
}

@Article{Sandor:1996:CIM,
  author =       "J. S{\'a}ndor",
  title =        "On Certain Inequalities for Means, {II}",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "199",
  number =       "2",
  pages =        "629--635",
  year =         "1996",
  CODEN =        "JMANAK",
  DOI =          "http://dx.doi.org/10.1006/jmaa.1996.0165",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X96901651",
  abstract =     "A method based on sequences is applied to derive
                 inequalities between the arithmetic--geometric mean of
                 Gauss, the logarithmic mean, and certain other means.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@Article{Ba:1997:SMA,
  author =       "Dalahu Ba",
  title =        "Some mixed arithmetic--geometric mean inequalities
                 containing parameters and their applications",
  journal =      "Neimenggu Daxue Xuebao Ziran Kexue",
  volume =       "28",
  number =       "6",
  pages =        "731--734",
  year =         "1997",
  CODEN =        "NDZKEJ",
  ISSN =         "1000-1638",
  MRclass =      "26D15",
  MRnumber =     "1620953",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Neimenggu Daxue Xuebao. Ziran Kexue. Acta Scientiarum
                 Naturalium Universitatis Neimenggu",
}

@InProceedings{Borwein:1997:AGMa,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:1997:PS",
  pages =        "537--552",
  year =         "1997",
  DOI =          "http://dx.doi.org/10.1007/978-1-4757-2736-4_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56",
  acknowledgement = ack-nhfb,
}

@Article{Borwein:1997:AGMb,
  author =       "Jonathan A. Borwein and Petr Lison{\v{e}}k and John A.
                 Macdonald",
  title =        "Arithmetic--Geometric Means Revisited",
  journal =      j-MAPLE-TECH-NEWS,
  volume =       "4",
  number =       "1",
  pages =        "20--27",
  month =        "Winter",
  year =         "1997",
  ISSN =         "1061-5733",
  ISSN-L =       "1061-5733",
  bibdate =      "Wed Jul 23 09:11:50 1997",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
  note =         "Special issue on Maple in the mathematical sciences.",
  URL =          "http://docserver.carma.newcastle.edu.au/4/",
  acknowledgement = ack-nhfb,
  fjournal =     "Maple technical newsletter",
  journal-URL =  "http://web.mit.edu/maple/www/plibrary/mtn.html",
}

@InProceedings{Cox:1997:AGM,
  author =       "David A. Cox",
  title =        "The Arithmetic--Geometric Mean of Gauss",
  crossref =     "Berggren:1997:PS",
  pages =        "481--536",
  year =         "1997",
  DOI =          "http://dx.doi.org/10.1007/978-1-4757-2736-4_55",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_55",
  acknowledgement = ack-nhfb,
}

@Article{Dmitrieva:1997:FAB,
  author =       "O. M. Dmitrieva and V. N. Maloz{\"e}mov",
  title =        "On a fast algorithm based on arithmetic--geometric
                 means",
  journal =      j-ZH-VYCHISL-MAT-MAT-FIZ,
  volume =       "37",
  number =       "3",
  pages =        "277--290",
  year =         "1997",
  CODEN =        "ZVMFAN",
  ISSN =         "0044-4669",
  MRclass =      "65B99 (11Y60 33E05 65D20)",
  MRnumber =     "1452573",
  MRreviewer =   "Gh. Adam",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Zhurnal Vychislitel\cprime no\u\i\ Matematiki i
                 Matematichesko\u\i\ Fiziki. Rossi\u\i skaya Akademiya
                 Nauk",
  journal-URL =  "http://www.mathnet.ru/zvmmf",
}

@Article{Nishiwada:1997:AAG,
  author =       "Kimimasa Nishiwada",
  title =        "Algorithm of the arithmetic--geometric mean and its
                 complex limits",
  journal =      j-HOKKAIDO-MATH-J,
  volume =       "26",
  number =       "3",
  pages =        "541--564",
  year =         "1997",
  CODEN =        "HMAJDN",
  DOI =          "http://dx.doi.org/10.14492/hokmj/1351258265",
  ISSN =         "0385-4035",
  MRclass =      "11F99 (11F06 33E05 40A05)",
  MRnumber =     "1483461",
  MRreviewer =   "D. C. Russell",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Hokkaido Mathematical Journal",
  journal-URL =  "http://projecteuclid.org/hokmj",
}

@InProceedings{Salamin:1997:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ Using Arithmetic--Geometric
                 Mean",
  crossref =     "Berggren:1997:PS",
  pages =        "418--423",
  year =         "1997",
  DOI =          "http://dx.doi.org/10.1007/978-1-4757-2736-4_46",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_46",
  acknowledgement = ack-nhfb,
}

@Article{Seiffert:1997:TIA,
  author =       "H. J. Seiffert",
  title =        "Three inequalities for the arithmetic, identric, and
                 geometric means",
  journal =      j-SIAM-REVIEW,
  volume =       "39",
  number =       "2",
  pages =        "330--332",
  month =        "????",
  year =         "1997",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "June 1997",
  xxnote =       "Check title word: identric??",
}

@Article{Bencze:1998:NPA,
  author =       "Mih{\'a}ly Bencze",
  title =        "A new proof of the arithmetic--geometric mean
                 inequality",
  journal =      j-OCTOGON-MATH-MAG,
  volume =       "6",
  number =       "1",
  pages =        "49--50",
  year =         "1998",
  ISSN =         "1222-5657 (print), 2248-1893 (electronic)",
  MRclass =      "26D15",
  MRnumber =     "1630953",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Octogon Mathematical Magazine",
}

@Book{Borwein:1998:PAS,
  author =       "Jonathan M. Borwein and Peter B. Borwein",
  title =        "Pi and the {AGM}: A study in analytic number theory
                 and computational complexity",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xvi + 414",
  year =         "1998",
  ISBN =         "0-471-31515-X",
  ISBN-13 =      "978-0-471-31515-5",
  MRclass =      "11Y60 (11B65 68Q25)",
  MRnumber =     "1641658",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Reprint of the 1987 original.",
  series =       "Canadian Mathematical Society Series of Monographs and
                 Advanced Texts, 4",
  acknowledgement = ack-nhfb,
}

@Article{Kosaki:1998:AGM,
  author =       "Hideki Kosaki",
  title =        "Arithmetic--Geometric Mean and Related Inequalities
                 for Operators",
  journal =      j-J-FUNCT-ANAL,
  volume =       "156",
  number =       "2",
  pages =        "429--451",
  year =         "1998",
  CODEN =        "JFUAAW",
  DOI =          "http://dx.doi.org/10.1006/jfan.1998.3258",
  ISSN =         "0022-1236 (print), 1096-0783 (electronic)",
  ISSN-L =       "0022-1236",
  MRclass =      "47A63 (47A30)",
  MRnumber =     "1636964",
  MRreviewer =   "Takayuki Furuta",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S002212369893258X",
  abstract =     "In recent years certain arithmetic--geometric mean and
                 related inequalities for operators and unitarily
                 invariant norms have been obtained by many authors
                 based on majorization technique and so on. We first
                 point out that they are direct consequences of integral
                 expressions of relevant operators. Furthermore we
                 obtain related new inequalities (Theorems 4, 5, and 6)
                 based on our current approach.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Functional Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00221236",
}

@Article{Maligranda:1998:WHI,
  author =       "Lech Maligranda",
  title =        "Why {H{\"o}lder's Inequality} should be called
                 {Rogers' Inequality}",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "1",
  number =       "1",
  pages =        "69--83",
  month =        "????",
  year =         "1998",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  ISSN-L =       "1331-4343",
  bibdate =      "Fri Feb 15 16:18:07 2013",
  bibsource =    "http://mia.ele-math.com/;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  ZMnumber =     "0889.26001",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Inequal. Appl.",
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
  keywords =     "H{\"o}lder inequality; Cauchy inequality; Jensen
                 inequality; history; biographies",
  ZMclass =      "26-03 (Historical (real functions)); 26D15
                 (Inequalities for sums, series and integrals of real
                 functions); 01A50 (Mathematics in the 18th century);
                 01A60 (Mathematics in the 20th century); 01A70
                 (Biographies, obituaries, personalia, bibliographies)",
  ZMreviewer =   "Johann Acz{\'e}l (Waterloo/Ontario)",
}

@Article{Sole:1998:LCA,
  author =       "P. Sol{\'e} and P. Loyer",
  title =        "{$ U_n $} Lattices, Construction {$B$}, and {AGM}
                 Iterations",
  journal =      j-EUR-J-COMB,
  volume =       "19",
  number =       "2",
  pages =        "227--236",
  month =        feb,
  year =         "1998",
  CODEN =        "EJOCDI",
  DOI =          "http://dx.doi.org/10.1006/eujc.1997.0185",
  ISSN =         "0195-6698 (print), 1095-9971 (electronic)",
  ISSN-L =       "0195-6698",
  bibdate =      "Tue Mar 14 17:10:52 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "European Journal of Combinatorics",
}

@Article{Toader:1998:SMV,
  author =       "Gh. Toader",
  title =        "Some Mean Values Related to the Arithmetic--Geometric
                 Mean",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "218",
  number =       "2",
  pages =        "358--368",
  year =         "1998",
  CODEN =        "JMANAK",
  DOI =          "http://dx.doi.org/10.1006/jmaa.1997.5766",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "26D15 (39B22)",
  MRnumber =     "1606799",
  MRreviewer =   "Zsolt P{\'a}les",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X97957668",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@TechReport{Boldo:1999:CRE,
  author =       "Sylvie Boldo",
  title =        "Calcul rapide et exact de fonctions
                 {\'e}l{\'e}mentaires en pr{\'e}cision arbitraire par la
                 moyenne arithm{\'e}tico-g{\'e}om{\'e}trique. ({French})
                 [Rapid and exact computation of elementary functions in
                 arbitrary precision by the arithmetic--geometric
                 mean]",
  type =         "Report",
  institution =  "INRIA, Projet Spaces, LORIA, Campus Scientifique",
  address =      "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
                 France",
  pages =        "29",
  year =         "1999",
  bibdate =      "Tue Nov 23 11:00:03 2004",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Under the direction of Paul Zimmermann.",
  URL =          "http://perso.ens-lyon.fr/sylvie.boldo/doc/mpfr.ps",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Article{Cass:1999:BRP,
  author =       "Peter Cass",
  title =        "Book Review: {{\booktitle{Pi and the AGM}}}",
  journal =      j-MATH-GAZ,
  volume =       "83",
  number =       "497",
  pages =        "334--335",
  month =        jul,
  year =         "1999",
  CODEN =        "MAGAAS",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Sat Aug 13 18:09:13 MDT 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/3619084",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@Article{Donagi:1999:AGM,
  author =       "Ron Donagi and Ron Livn{\'e}",
  title =        "The arithmetic--geometric mean and isogenies for
                 curves of higher genus",
  journal =      j-ANN-SC-NORM-SUPER-PISA-CL-SCI,
  volume =       "28",
  number =       "2",
  pages =        "323--339",
  year =         "1999",
  CODEN =        "PSNAAI",
  ISSN =         "0391-173x (print), 2036-2145 (electronic)",
  ISSN-L =       "0391-173X",
  MRclass =      "14H40 (14K02)",
  MRnumber =     "1736231",
  MRreviewer =   "Arnaud Beauville",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.numdam.org/item?id=ASNSP_1999_4_28_2_323_0",
  acknowledgement = ack-nhfb,
  fjournal =     "Annali della Scuola Normale Superiore di Pisa. Classe
                 di Scienze. Serie IV",
}

@Article{Hiai:1999:CVM,
  author =       "Fumio Hiai and Hideki Kosaki",
  title =        "Comparison of Various Means for Operators",
  journal =      j-J-FUNCT-ANAL,
  volume =       "163",
  number =       "2",
  pages =        "300--323",
  year =         "1999",
  CODEN =        "JFUAAW",
  DOI =          "http://dx.doi.org/10.1006/jfan.1998.3375",
  ISSN =         "0022-1236 (print), 1096-0783 (electronic)",
  ISSN-L =       "0022-1236",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022123698933754",
  abstract =     "For Hilbert space operators $H$, $K$, $X$ with $ H, K
                 \geq 0$ the norm inequality $ |||H^{1 / 2} X K^{1 /
                 2}||| \leq (1 / 2) |||H X + X K|||$ is known, where |||
                 \cdot ||| is an arbitrary unitarily invariant norm. A
                 refinement of this arithmetic--geometric mean
                 inequality is studied. Similar norm inequalities are
                 indeed established for various natural means for
                 operators such as the logarithmic mean.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of functional analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00221236",
}

@Article{Kittaneh:1999:SNI,
  author =       "Fuad Kittaneh",
  title =        "Some norm inequalities for operators",
  journal =      j-CAN-MATH-BULL,
  volume =       "42",
  number =       "1",
  pages =        "87--96",
  month =        mar,
  year =         "1999",
  CODEN =        "CMBUA3",
  DOI =          "http://dx.doi.org/10.4153/CMB-1999-010-6",
  ISSN =         "0008-4395 (print), 1496-4287 (electronic)",
  ISSN-L =       "0008-4395",
  MRclass =      "47A30, 47B10, 47B15, 47B20",
  bibdate =      "Thu Sep 8 10:22:25 MDT 2011",
  bibsource =    "http://cms.math.ca/cmb/v42/;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/canmathbull.bib",
  abstract =     "Let $ A_i $, $ B_i $ and $ X_i $ $ (i = 1, 2, \dots,
                 n) $ be operators on a separable Hilbert space. It is
                 shown that if $f$ and $g$ are nonnegative continuous
                 functions on $ [0, \infty)$ which satisfy the relation
                 $ f(t)g(t) = t$ for all $t$ in $ [0, \infty)$, then $$
                 \Biglvert \, \Bigl | \sum^n_{i = 1} A^*_i X_i B_i \Bigr
                 |^r \, \Bigrvert^2 \leq \Biglvert \Bigl (\sum^n_{i = 1}
                 A^*_i f (|X^*_i|)^2 A_i \Bigr)^r \Bigrvert \, \Biglvert
                 \Bigl (\sum^n_{i = 1} B^*_i g (|X_i|)^2 B_i \Bigr)^r
                 \Bigrvert $$ for every $ r > 0$ and for every unitarily
                 invariant norm. This result improves some known
                 Cauchy--Schwarz type inequalities. Norm inequalities
                 related to the arithmetic--geometric mean inequality
                 and the classical Heinz inequalities are also
                 obtained.",
  acknowledgement = ack-nhfb,
  ams-subject-primary = "47A30, 47B10, 47B15, 47B20",
  fjournal =     "Canadian Mathematical Bulletin. Bulletin Canadien de
                 Math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cmb/",
  journalabbrev = "CMB",
  keywords =     "arithmetic--geometric mean inequality; Cauchy--Schwarz
                 inequality; Heinz inequality; positive operator;
                 Unitarily invariant norm",
  refnum =       "7284",
}

@Article{Sandor:1999:AGM,
  author =       "J{\'o}zsef S{\'a}ndor",
  title =        "On the arithmetic--geometric mean of {Gauss}",
  journal =      j-OCTOGON-MATH-MAG,
  volume =       "7",
  number =       "1",
  pages =        "108--115",
  year =         "1999",
  ISSN =         "1222-5657 (print), 2248-1893 (electronic)",
  MRclass =      "26D15",
  MRnumber =     "1730039",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Octogon Mathematical Magazine",
}

@Article{Alsina:2000:PWA,
  author =       "Claudi Alsina",
  title =        "Proof without Words: The Arithmetic--Geometric Mean
                 Inequality for Three Positive Numbers",
  journal =      j-MATH-MAG,
  volume =       "73",
  number =       "2",
  pages =        "97",
  year =         "2000",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  MRclass =      "Contributed Item",
  MRnumber =     "1573443",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2691079?origin=pubexport",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@Article{Bhatia:2000:NMA,
  author =       "Rajendra Bhatia and Fuad Kittaneh",
  title =        "Notes on matrix arithmetic--geometric mean
                 inequalities",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "308",
  number =       "1--3",
  pages =        "203--211",
  day =          "15",
  month =        mar,
  year =         "2000",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/S0024-3795(00)00048-3",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A45 (15A42 15A60 47A30)",
  MRnumber =     "1751140",
  MRreviewer =   "Yao Zhang",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala2000.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/30/19/125/25/36/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/30/19/125/25/36/article.pdf;
                 http://www.sciencedirect.com/science/article/pii/S0024379500000483",
  abstract =     "For positive semi-definite $ n \times n $ matrices,
                 the inequality $ 4 ||| A B ||| \leq ||| (A + B)^2 ||| $
                 is shown to hold for every unitarily invariant norm.
                 The connection of this with some other matrix
                 arithmetic--geometric mean inequalities and trace
                 inequalities is discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric mean; Majorisation; Singular
                 values; Unitarily invariant norms",
}

@InProceedings{Borwein:2000:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:2000:PS",
  pages =        "537--552",
  year =         "2000",
  DOI =          "http://dx.doi.org/10.1007/978-1-4757-3240-5_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_56",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cox:2000:AGM,
  author =       "David A. Cox",
  title =        "The Arithmetic--Geometric Mean of {Gauss}",
  crossref =     "Berggren:2000:PS",
  pages =        "481--536",
  year =         "2000",
  DOI =          "http://dx.doi.org/10.1007/978-1-4757-3240-5_55",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_55",
  acknowledgement = ack-nhfb,
}

@InCollection{Kwon:2000:AGM,
  author =       "Ern Gun Kwon and Kwang Ho Shon",
  booktitle =    "Finite or infinite dimensional complex analysis
                 ({Fukuoka}, 1999)",
  title =        "On the arithmetic--geometric mean inequality",
  volume =       "214",
  publisher =    "Dekker, New York",
  pages =        "233--235",
  year =         "2000",
  MRclass =      "26D15",
  MRnumber =     "1771322",
  MRreviewer =   "L. Losonczi",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Lecture Notes in Pure and Appl. Math.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Salamin:2000:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ Using Arithmetic--Geometric
                 Mean",
  crossref =     "Berggren:2000:PS",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "418--423",
  year =         "2000",
  DOI =          "http://dx.doi.org/10.1007/978-1-4757-3240-5_46",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-3240-5_46",
  acknowledgement = ack-nhfb,
}

@Article{Sury:2000:AGM,
  author =       "B. Sury",
  title =        "The arithmetico--geometric mean of {Gauss}: How to
                 find the perimeter of an ellipse",
  journal =      j-RESONANCE,
  volume =       "5",
  number =       "8",
  pages =        "72--83",
  month =        aug,
  year =         "2000",
  CODEN =        "RESOFE",
  DOI =          "http://dx.doi.org/10.1007/bf02837938",
  ISSN =         "0971-8044 (print), 0973-712X (electronic)",
  bibdate =      "Tue Mar 14 15:45:02 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Resonance",
  journal-URL =  "http://link.springer.com/journal/12045",
}

@Article{Wachspress:2000:EEF,
  author =       "E. L. Wachspress",
  title =        "Evaluating elliptic functions and their inverses",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "39",
  number =       "3--4",
  pages =        "131--136",
  month =        feb,
  year =         "2000",
  CODEN =        "CMAPDK",
  DOI =          "http://dx.doi.org/10.1016/S0898-1221(99)00339-9",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:06 MST 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122199003399",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "arithmetic--geometric mean (AGM)",
}

@Article{Yang:2000:AGM,
  author =       "Ling Ou Yang",
  title =        "Arithmetic--geometric mean inequalities for trace of
                 operators",
  journal =      "Math. Theory Appl. (Changsha)",
  volume =       "20",
  number =       "3",
  pages =        "117--120",
  year =         "2000",
  ISSN =         "1006-8074",
  MRclass =      "47A64 (47A63)",
  MRnumber =     "1806708",
  MRreviewer =   "Frank Hansen",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Theory and Applications",
}

@Article{Bracken:2001:AGM,
  author =       "Paul Bracken",
  title =        "An arithmetic--geometric mean inequality",
  journal =      j-EXPO-MATH,
  volume =       "19",
  number =       "3",
  pages =        "273--279",
  year =         "2001",
  DOI =          "http://dx.doi.org/10.1016/S0723-0869(01)80006-2",
  ISSN =         "0723-0869 (print), 1878-0792 (electronic)",
  ISSN-L =       "0723-0869",
  MRclass =      "26D15",
  MRnumber =     "1852077",
  MRreviewer =   "Antal Bege",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0723086901800062",
  abstract =     "Several integrals which are related to the
                 arithmetic--geometric mean are developed and proved in
                 a very elementary way. These results can be used to
                 prove a known inequality which relates this mean to the
                 logarithmic mean.",
  acknowledgement = ack-nhfb,
  fjournal =     "Expositiones Mathematicae",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07230869",
}

@Article{Dobbs:2001:PAG,
  author =       "David E. Dobbs",
  title =        "A proof of the arithmetic--geometric mean inequality
                 using non-{Euclidean} geometry",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "32",
  number =       "5",
  pages =        "778--782",
  year =         "2001",
  CODEN =        "IJMEBM",
  DOI =          "http://dx.doi.org/10.1080/002073901753124655",
  ISSN =         "0020-739x (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  MRclass =      "26D15 (51M10)",
  MRnumber =     "1862675",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  journal-URL =  "http://www.tandfonline.com/loi/tmes20",
}

@Article{Ekart:2001:NGA,
  author =       "Anik{\'o} Ek{\'a}rt and S. Z. N{\'e}meth",
  title =        "A noncontinuous generalization of the
                 arithmetic--geometric mean",
  journal =      j-APPL-MATH-COMP,
  volume =       "124",
  number =       "2",
  pages =        "261--279",
  day =          "25",
  month =        oct,
  year =         "2001",
  CODEN =        "AMHCBQ",
  DOI =          "http://dx.doi.org/10.1016/S0096-3003(00)00098-9",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "40A05",
  MRnumber =     "1857690",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.elsevier.com/locate/issn/00963003;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib",
  URL =          "http://www.elsevier.com/gej-ng/10/9/12/113/31/36/abstract.html;
                 http://www.sciencedirect.com/science/article/pii/S0096300300000989",
  abstract =     "The notions of prickly set, scalar and vectorial mean
                 are defined. A noncontinuous generalization of the
                 arithmetic--geometric mean is given, by considering the
                 recursion xn+1=F(xn), where F:C \to C is a vectorial
                 mean and C is a closed prickly subset of Rm. The
                 convergence of this recursion is proved and it is shown
                 that the limit is contained in the diagonal of C. If F
                 is continuous, it is deduced that the limit of the
                 recursion is a continuous function of the initial value
                 x=x0. Denoting the limit by F\infty(x) it is proved
                 that if F is monotone, then F\infty it is also monotone
                 (where the monotonicity is considered with respect to
                 the closed cone R+m).",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "Arithmetic--geometric mean; F-mean; Prickly set;
                 Scalar mean; Vectorial mean",
}

@Article{Nakamura:2001:AAA,
  author =       "Yoshimasa Nakamura",
  title =        "Algorithms associated with arithmetic, geometric and
                 harmonic means and integrable systems",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "131",
  number =       "1--2",
  pages =        "161--174",
  day =          "1",
  month =        jun,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:18 MST 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 http://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700003162",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Sury:2001:LA,
  author =       "B. Sury",
  title =        "Logarithm and {AGM}",
  journal =      j-RESONANCE,
  volume =       "6",
  number =       "11",
  pages =        "85--86",
  month =        nov,
  year =         "2001",
  CODEN =        "RESOFE",
  DOI =          "http://dx.doi.org/10.1007/bf02868248",
  ISSN =         "0971-8044 (print), 0973-712X (electronic)",
  bibdate =      "Tue Mar 14 15:35:34 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Resonance",
  journal-URL =  "http://link.springer.com/journal/12045",
}

@Article{Yang:2001:AGM,
  author =       "Hansheng Yang and Heng Yang",
  title =        "The Arithmetic--Geometric Mean Inequality and the
                 Constant $e$",
  journal =      j-MATH-MAG,
  volume =       "74",
  number =       "4",
  pages =        "321--323",
  year =         "2001",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  MRclass =      "Contributed Item",
  MRnumber =     "1573553",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.jstor.org/stable/2691107?origin=pubexport",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@Article{Disch:2002:CPV,
  author =       "Burkhard Disch",
  title =        "Computing present values by the {AGM}",
  journal =      "{Bl{\"a}tter der DGVFM}",
  volume =       "25",
  number =       "4",
  pages =        "831--849",
  month =        oct,
  year =         "2002",
  DOI =          "http://dx.doi.org/10.1007/bf02809119",
  bibdate =      "Tue Mar 14 15:31:34 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Gaudry:2002:CCS,
  author =       "Pierrick Gaudry",
  booktitle =    "{International Conference on the Theory and
                 Application of Cryptology and Information Security:
                 ASIACRYPT 2002: Advances in Cryptology --- ASIACRYPT
                 2002}",
  title =        "A Comparison and a Combination of {SST} and {AGM}
                 Algorithms for Counting Points of Elliptic Curves in
                 Characteristic $2$",
  volume =       "2501",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "311--327",
  year =         "2002",
  CODEN =        "LNCSD9",
  DOI =          "http://dx.doi.org/10.1007/3-540-36178-2_20",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Mar 14 15:33:17 2017",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2501.htm;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 http://www.math.utah.edu/pub/tex/bib/lncs2002e.bib",
  series =       "Lecture Notes in Computer Science",
  URL =          "http://link.springer.de/link/service/series/0558/bibs/2501/25010311.htm;
                 http://link.springer.de/link/service/series/0558/papers/2501/25010311.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Xie:2002:SGA,
  author =       "Ziqing Xie",
  title =        "On the Summation of Generalized Arithmetic--Geometric
                 Trigonometric Series",
  journal =      j-FIB-QUART,
  volume =       "40",
  number =       "2",
  pages =        "128--135",
  month =        may,
  year =         "2002",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:03:33 MDT 2011",
  bibsource =    "http://www.fq.math.ca/40-2.html;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/40-2/xie.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Unpublished{Borwein:2003:ACFa,
  author =       "Jonathan M. Borwein",
  title =        "The {AGM} Continued Fraction of {Ramanujan}",
  day =          "31",
  month =        jul,
  year =         "2003",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "CECM Day 2003, Simon Fraser University, Burnaby, BC,
                 Canada.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:2003:ACFb,
  author =       "Jonathan M. Borwein",
  title =        "The {AGM} Continued Fraction of {Ramanujan}",
  day =          "16",
  month =        sep,
  year =         "2003",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "First Plenary Lecture, First Congress of the
                 Mathematical Society of South East Europe (MASSE{\'E}),
                 Borovets, Bulgaria.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:2003:ACFc,
  author =       "Jonathan M. Borwein",
  title =        "The {AGM} Continued Fraction of {Ramanujan}",
  day =          "14",
  month =        oct,
  year =         "2003",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, Reed College, OR, USA.",
  acknowledgement = ack-nhfb,
}

@Article{Gluskin:2003:NGA,
  author =       "E. Gluskin and V. Milman",
  title =        "Note on the Geometric--Arithmetic Mean Inequality",
  journal =      j-LECT-NOTES-MATH,
  volume =       "1807",
  pages =        "131--135",
  year =         "2003",
  CODEN =        "LNMAA2",
  DOI =          "http://dx.doi.org/10.1007/978-3-540-36428-3_11",
  ISBN =         "3-540-00485-8 (print), 3-540-36428-5 (e-book)",
  ISBN-13 =      "978-3-540-00485-1 (print), 978-3-540-36428-3
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  bibdate =      "Fri May 9 19:07:18 MDT 2014",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/lnm2000.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-540-36428-3_11/",
  acknowledgement = ack-nhfb,
  book-DOI =     "http://dx.doi.org/10.1007/b10415",
  book-URL =     "http://www.springerlink.com/content/978-3-540-36428-3",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}

@Article{Knockaert:2003:BUB,
  author =       "Luc Knockaert",
  title =        "Best upper bounds based on the arithmetic--geometric
                 mean inequality",
  journal =      j-ARCH-INEQUAL-APPL,
  volume =       "1",
  number =       "1",
  pages =        "85--90",
  year =         "2003",
  ISSN =         "1542-6149",
  MRclass =      "15A42 (15A12 60E15)",
  MRnumber =     "1992268",
  MRreviewer =   "E. Seneta",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Archives of Inequalities and Applications. An
                 International Journal for Theory and Applications",
}

@Article{Monhor:2003:AGM,
  author =       "D. Monhor",
  title =        "The arithmetic--geometric mean and the elliptic mean
                 error",
  journal =      j-ACTA-GEOD-GEOPHYS-HU,
  volume =       "38",
  number =       "1",
  pages =        "??--??",
  month =        feb,
  year =         "2003",
  CODEN =        "AGGHFW",
  DOI =          "http://dx.doi.org/10.1556/AGeod.38.2003.1.8",
  ISSN =         "1217-8977 (print), 1587-1037 (electronic)",
  ISSN-L =       "1217-8977",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/article/10.1556/AGeod.38.2003.1.8",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Geodaetica et Geophysica Hungarica",
  journal-URL =  "http://www.akademiai.com/loi/074",
  remark =       "Journal archive contains only years 2001 to date.",
}

@Article{Rooin:2003:AIB,
  author =       "Jamal Rooin",
  title =        "{AGM} inequality with binomial expansion",
  journal =      j-ELEM-MATH,
  volume =       "58",
  number =       "3",
  pages =        "115--117",
  month =        aug,
  year =         "2003",
  DOI =          "http://dx.doi.org/10.1007/s00017-003-0188-x",
  ISSN =         "0013-6018 (print), 1420-8962 (electronic)",
  ISSN-L =       "0013-6018",
  bibdate =      "Tue Mar 14 15:30:54 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik",
}

@InProceedings{Borwein:2004:AGMa,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:2004:PSB",
  pages =        "537--552",
  year =         "2004",
  DOI =          "http://dx.doi.org/10.1007/978-1-4757-4217-6_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_56",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:2004:RACa,
  author =       "Jonathan M. Borwein",
  title =        "{Ramanujan}'s {AGM} Continued Fractions and Dynamics:
                 the real case",
  day =          "4",
  month =        mar,
  year =         "2004",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Colloquium, Mathematics Department, Dalhousie
                 University, Halifax, NS, Canada.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:2004:RACb,
  author =       "Jonathan M. Borwein",
  title =        "{Ramanujan}'s {AGM} Continued Fractions and Dynamics:
                 the complex case",
  day =          "10",
  month =        mar,
  year =         "2004",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Analysis Seminar, Mathematics Department, Dalhousie
                 University, Halifax, NS, Canada.",
  acknowledgement = ack-nhfb,
}

@Unpublished{Borwein:2004:RACc,
  author =       "Jonathan M. Borwein",
  title =        "{Ramanujan}'s {AGM} Continued Fractions and Dynamics",
  day =          "27",
  month =        aug,
  year =         "2004",
  bibdate =      "Tue Aug 16 10:19:46 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Workshop on Analytic and Computational Number Theory,
                 August 23--27, Dalhousie University, Halifax, NS,
                 Canada.",
  acknowledgement = ack-nhfb,
}

@Article{Borwein:2004:RAFa,
  author =       "J. Borwein and R. Crandall and G. Fee",
  title =        "On the {Ramanujan} {AGM} fraction. {I}. {The}
                 real-parameter case",
  journal =      j-EXP-MATH,
  volume =       "13",
  number =       "3",
  pages =        "275--285",
  month =        "????",
  year =         "2004",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1080/10586458.2004.10504540",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11J70 (11A55 33C05 40A15)",
  MRnumber =     "2103326 (2005g:11126)",
  MRreviewer =   "James G. Mc Laughlin",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/expmath.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/27/;
                 http://projecteuclid.org/euclid.em/1103749836",
  acknowledgement = ack-nhfb,
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
}

@Article{Borwein:2004:RAFb,
  author =       "J. Borwein and R. Crandall",
  title =        "On the {Ramanujan} {AGM} fraction. {II}. {The}
                 complex-parameter case",
  journal =      j-EXP-MATH,
  volume =       "13",
  number =       "3",
  pages =        "287--295",
  month =        "????",
  year =         "2004",
  CODEN =        "????",
  DOI =          "http://dx.doi.org/10.1080/10586458.2004.10504541",
  ISSN =         "1058-6458 (print), 1944-950X (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "11J70 (11A55 33C05)",
  MRnumber =     "2103327 (2005h:11149)",
  MRreviewer =   "James G. Mc Laughlin",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/expmath.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/29/;
                 http://projecteuclid.org/euclid.em/1103749837",
  acknowledgement = ack-nhfb,
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
}

@InProceedings{Cox:2004:AGM,
  author =       "David A. Cox",
  title =        "The Arithmetic--Geometric Mean of {Gauss}",
  crossref =     "Berggren:2004:PSB",
  pages =        "481--536",
  year =         "2004",
  DOI =          "http://dx.doi.org/10.1007/978-1-4757-4217-6_55",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_55",
  acknowledgement = ack-nhfb,
}

@InProceedings{Salamin:2004:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ Using Arithmetic--Geometric
                 Mean",
  crossref =     "Berggren:2004:PSB",
  pages =        "418--423",
  year =         "2004",
  DOI =          "http://dx.doi.org/10.1007/978-1-4757-4217-6_46",
  bibdate =      "Tue Mar 14 11:58:19 MDT 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-4217-6_46",
  acknowledgement = ack-nhfb,
}

@Misc{Tkachev:2003:EFI,
  author =       "Vladimir G. Tkachev",
  title =        "Elliptic functions: Introduction course",
  howpublished = "Web lecture notes.",
  day =          "25",
  month =        nov,
  year =         "2003",
  bibdate =      "Wed Mar 15 08:43:21 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://users.mai.liu.se/vlatk48/teaching/lect2-agm.pdf",
  acknowledgement = ack-nhfb,
  tableofcontents = "Chapter 1. Elliptic integrals and Jacobi's theta
                 functions / 5 \\
                 1.1. Elliptic integrals and the AGM: real case / 5 \\
                 1.1.3. The arithmetic-geometric mean iteration / 7 \\
                 1.2. Lemniscates and elastic curves / 11 \\
                 1.3. Euler's addition theorem / 18 \\
                 1.4. Theta functions: preliminaries 5 / 24 \\
                 Chapter 2. General theory of doubly periodic functions
                 / 31 \\
                 2.1. Preliminaries / 31 \\
                 2.2. Periods of analytic functions / 33 \\
                 2.3. Existence of doubly periodic functions / 36 \\
                 2.4. Liouville's theorems / 38 \\
                 2.5. The Weierstrass function $\wp(z)$ / 43 \\
                 2.6. Modular forms / 51 \\
                 Bibliography / 61",
}

@Article{Wu:2005:SRE,
  author =       "Shanhe Wu",
  title =        "Some results on extending and sharpening the
                 {Weierstrass} product inequalities",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "308",
  number =       "2",
  pages =        "689--702",
  year =         "2005",
  CODEN =        "JMANAK",
  DOI =          "http://dx.doi.org/10.1016/j.jmaa.2004.11.064",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X04010157",
  abstract =     "In this paper, we establish two extensions of
                 Weierstrass's inequality involving symmetric functions
                 by means of the theory of majorization, and give an
                 interesting sharpness of Weierstrass's inequality by
                 using the arithmetic--geometric mean inequality.
                 Furthermore, we apply these results to improve a
                 well-known inequality and deduce some new
                 inequalities.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Arithmetic--geometric mean inequality; Elementary
                 symmetric function; Majorization; Schur-concave
                 function; Weierstrass's inequality",
}

@Article{Bhatia:2006:IAG,
  author =       "Rajendra Bhatia",
  title =        "Interpolating the arithmetic--geometric mean
                 inequality and its operator version",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "413",
  number =       "2--3",
  pages =        "355--363",
  day =          "1",
  month =        mar,
  year =         "2006",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2005.03.005",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "47A63 (15A48)",
  MRnumber =     "2198940",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala2000.bib",
  note =         "Special Issue on the 11th Conference of the
                 International Linear Algebra Society, Coimbra, 200411th
                 Conference of the International Linear Algebra Society,
                 Coimbra, 2004",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379505001382",
  abstract =     "Two families of means (called Heinz means and Heron
                 means) that interpolate between the geometric and the
                 arithmetic mean are considered. Comparison inequalities
                 between them are established. Operator versions of
                 these inequalities are obtained. Failure of such
                 extensions in some cases is illustrated by a simple
                 example.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Inequalities for means; Operator inequalities;
                 Positive definite matrix; Unitarily invariant norm",
}

@Article{Enge:2006:CCP,
  author =       "Andreas Enge",
  title =        "The complexity of class polynomial computation via
                 floating point approximations",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "24",
  month =        jan,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in Mathematics of Computation 78, {\bf 266}
                 (2009) 1089--1107.",
  URL =          "http://arxiv.org/abs/cs/0601104",
  abstract =     "We analyse the complexity of computing class
                 polynomials, that are an important ingredient for CM
                 constructions of elliptic curves, via complex floating
                 point approximations of their roots. The heart of the
                 algorithm is the evaluation of modular functions in
                 several arguments. The fastest one of the presented
                 approaches uses a technique devised by Dupont to
                 evaluate modular functions by Newton iterations on an
                 expression involving the arithmetic--geometric mean. It
                 runs in time $ O (|D| \log^5 |D| \log \log |D|) = O
                 (|D|^{1 + \epsilon }) = O (h^{2 + \epsilon }) $ for any
                 $ \epsilon > 0 $, where $D$ is the CM discriminant and
                 $h$ is the degree of the class polynomial. Another fast
                 algorithm uses multipoint evaluation techniques known
                 from symbolic computation; its asymptotic complexity is
                 worse by a factor of $ \log |D|$. Up to logarithmic
                 factors, this running time matches the size of the
                 constructed polynomials. The estimate also relies on a
                 new result concerning the complexity of enumerating the
                 class group of an imaginary-quadratic order and on a
                 rigorously proven upper bound for the height of class
                 polynomials.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (cs.NA); Symbolic Computation
                 (cs.SC); Number Theory (math.NT)",
}

@Article{Liu:2006:OTA,
  author =       "Lei Liu and Jian Hua Zhang",
  title =        "An operator-trace arithmetic--geometric mean
                 inequality",
  journal =      "J. Baoji Univ. Arts Sci. Math. Colloq. Chin. Univ.",
  number =       "3B",
  pages =        "208--209",
  year =         "2006",
  ISSN =         "1007-1261",
  MRclass =      "47A63",
  MRnumber =     "2268274",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Baoji University of Arts and Sciences. Math
                 Colloquium of Chinese Universities. Baoji Wenli Xueyuan
                 Xuebao. Daxue Shuxue Jikan",
}

@Article{Sabnis:2006:AAG,
  author =       "S. V. Sabnis and G. Agnihothram",
  title =        "Application of arithmetic--geometric mean inequality
                 for construction of reliability test plan for parallel
                 systems in the presence of covariates",
  journal =      j-ECON-QUAL-CONTROL,
  volume =       "21",
  number =       "2",
  pages =        "219--230",
  year =         "2006",
  DOI =          "http://dx.doi.org/10.1515/EQC.2006.219",
  ISSN =         "0940-5151 (print), 1869-6147 (electronic)",
  MRclass =      "62N05 (62N03)",
  MRnumber =     "2364112",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Economic Quality Control",
  journal-URL =  "http://degruyter.com/eqc",
}

@Article{Tao:2006:MRS,
  author =       "Yunxing Tao",
  title =        "More results on singular value inequalities of
                 matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "416",
  number =       "2--3",
  pages =        "724--729",
  year =         "2006",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2005.12.017",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379506000024",
  abstract =     "The arithmetic--geometric mean inequality for singular
                 values due to Bhatia and Kittaneh says that $ 2 s_j (A
                 B^\star) \leq s_j (A^\star A + B^\star B) $, $ j = 1,
                 2, \ldots $ for any matrices $A$, $B$. We give a new
                 equivalent form and some relevant generalizations of
                 this inequality. In particular, we show that $ s_j
                 (A^{1 / 4} B^{3 / 4} + A^{3 / 4} B^{1 / 4}) \leq s_j (A
                 + B)$, $ j = 1, \ldots, n$ for any $ n \times n $
                 positive semidefinite matrices $A$, $B$, which proves a
                 special case of Zhan's conjecture posed in 2000.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric mean; Positive semidefinite
                 matrix; Singular value",
}

@Article{Yamazaki:2006:EKI,
  author =       "Takeaki Yamazaki",
  title =        "An extension of {Kantorovich} inequality to
                 $n$-operators via the geometric mean by
                 {Ando--Li--Mathias}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "416",
  number =       "2--3",
  pages =        "688--695",
  year =         "2006",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2005.12.013",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S002437950500604X",
  abstract =     "In this paper, we shall extend Kantorovich inequality.
                 This is an estimate by using the geometric mean of
                 n-operators which have been defined by
                 Ando--Li--Mathias in [T. Ando, C. K. Li, R. Mathias,
                 Geometric means, Linear Algebra Appl. 385 (2004)
                 305--334]. As a related result, we obtain a converse of
                 arithmetic--geometric means inequality of n-operators
                 via Kantorovich constant.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric means inequality; Geometric mean
                 of n-operators; Kantorovich inequality; Specht's
                 ratio",
}

@Article{Aujla:2007:EIC,
  author =       "Jaspal Singh Aujla and Jean-Christophe Bourin",
  title =        "Eigenvalue inequalities for convex and log-convex
                 functions",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "424",
  number =       "1",
  pages =        "25--35",
  year =         "2007",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2006.02.027",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "Special Issue in honor of Roger Horn",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379506001261",
  abstract =     "We give a matrix version of the scalar inequality $
                 f(a + b) \leq f(a) + f(b) $ for positive concave
                 functions $f$ on $ [0, \infty)$. We show that Choi's
                 inequality for positive unital maps and operator convex
                 functions remains valid for monotone convex functions
                 at the cost of unitary congruences. Some inequalities
                 for log-convex functions are presented and a new
                 arithmetic--geometric mean inequality for positive
                 matrices is given. We also point out a simple proof of
                 the Bhatia--Kittaneh arithmetic--geometric mean
                 inequality.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Convex function; Eigenvalue; Majorization; Unital
                 positive linear map",
}

@Article{Barnard:2007:IHA,
  author =       "Roger W. Barnard and Kendall C. Richards",
  title =        "On inequalities for hypergeometric analogues of the
                 arithmetic--geometric mean",
  journal =      j-JIPAM-J-INEQUAL-PURE-APPL-MATH,
  volume =       "8",
  number =       "3",
  pages =        "Article 65, 5",
  year =         "2007",
  ISSN =         "1443-5756",
  MRclass =      "26D15 (26E60 33C05)",
  MRnumber =     "2345920",
  MRreviewer =   "Giampietro Allasia",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "JIPAM. Journal of Inequalities in Pure and Applied
                 Mathematics",
  journal-URL =  "http://www.emis.de/journals/JIPAM/",
}

@Article{Hirschhorn:2007:GI,
  author =       "M. D. Hirschhorn",
  title =        "The {AM--GM} inequality",
  journal =      j-MATH-INTEL,
  volume =       "29",
  number =       "4",
  pages =        "7--??",
  month =        "????",
  year =         "2007",
  CODEN =        "MAINDC",
  DOI =          "http://dx.doi.org/10.1007/BF02986168",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  bibdate =      "Fri Feb 15 16:15:39 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  ZMnumber =     "1225.00022",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
  ZMclass =      "00A35 (Methodology of mathematics, didactics); 26D15
                 (Inequalities for sums, series and integrals of real
                 functions); 97I20 (Mappings and functions (educational
                 aspects))",
}

@Article{Kim:2007:CIH,
  author =       "Sejong Kim and Yongdo Lim",
  title =        "A converse inequality of higher order weighted
                 arithmetic and geometric means of positive definite
                 operators",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "426",
  number =       "2--3",
  pages =        "490--496",
  day =          "15",
  month =        oct,
  year =         "2007",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2007.05.028",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379507002455",
  abstract =     "In this paper we consider weighted arithmetic and
                 geometric means of higher orders constructed by the
                 symmetrization method appeared in Ando--Li--Mathias's
                 definition of multi-variable geometric means and the
                 arithmetic--geometric mean inequality of higher order
                 weighted version. We establish a converse inequality of
                 higher order weighed arithmetic and geometric means via
                 Specht ratio.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric mean inequality; Higher order
                 weighted geometric mean; Positive definite operator;
                 Specht ratio",
}

@Book{King:2007:DNC,
  author =       "Louis Vessot King",
  title =        "On the Direct Numerical Calculation of Elliptic
                 Functions and Integrals",
  publisher =    "Mellon Press",
  address =      "",
  pages =        "56",
  year =         "2007",
  ISBN =         "1-4067-4226-0",
  ISBN-13 =      "978-1-4067-4226-8",
  LCCN =         "",
  bibdate =      "Wed Feb 03 08:53:04 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  remark =       "The AGM method for Jacobian elliptic was discovered by
                 this book's author at McGill University in 1913, first
                 published in \cite{King:1921:SNF}, and then in a 1924
                 monograph, of which this is a reprint.",
}

@Article{Koike:2007:IFP,
  author =       "Kenji Koike and Hironori Shiga",
  title =        "Isogeny formulas for the {Picard} modular form and a
                 three terms arithmetic geometric mean",
  journal =      j-J-NUMBER-THEORY,
  volume =       "124",
  number =       "1",
  pages =        "123--141",
  year =         "2007",
  CODEN =        "JNUTA9",
  DOI =          "http://dx.doi.org/10.1016/j.jnt.2006.08.002",
  ISSN =         "0022-314x (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  MRclass =      "11F55",
  MRnumber =     "2320994",
  MRreviewer =   "Enrique Gonz{\'a}lez-Jim{\'e}nez",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X06002058",
  abstract =     "In this paper we study the Picard modular forms and
                 show a new three terms arithmetic geometric mean (AGM)
                 system. This AGM system is expressed via the Appell
                 hypergeometric function of two variables. The Picard
                 modular forms are expressed via the theta constants,
                 and they give the modular function for the family of
                 Picard curves. Our theta constants are ``Neben type''
                 modular forms of weight 1 defined on the complex
                 2-dimensional hyperball with respect to an index finite
                 subgroup of the Picard modular group. We define a
                 simultaneous 3-isogeny for the family of Jacobian
                 varieties of Picard curves. Our main theorem shows the
                 explicit relations between two systems of theta
                 constants which are corresponding to isogenous Jacobian
                 varieties. This relation induces a new three terms AGM
                 which is a generalization of Borweins' cubic AGM.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Lehavi:2007:EFA,
  author =       "D. Lehavi and C. Ritzenthaler",
  title =        "An Explicit Formula for the Arithmetic--Geometric Mean
                 in Genus $3$",
  journal =      j-EXP-MATH,
  volume =       "16",
  number =       "4",
  pages =        "421--440",
  month =        "????",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "1058-6458 (print), 1944-950x (electronic)",
  ISSN-L =       "1058-6458",
  MRclass =      "14H40 (14H45 14Q05)",
  MRnumber =     "2378484",
  MRreviewer =   "Mich{\`e}le Pelletier",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://projecteuclid.org/euclid.em;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/expmath.bib;
                 http://www.tandfonline.com/toc/uexm20/16/4",
  URL =          "http://projecteuclid.org/euclid.em/1204836513",
  acknowledgement = ack-nhfb,
  fjournal =     "Experimental Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/uexm20",
}

@Article{Tanimoto:2007:NOA,
  author =       "Shinji Tanimoto",
  title =        "A novel operation associated with {Gauss}'
                 arithmetic--geometric means",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--6",
  day =          "27",
  month =        aug,
  year =         "2007",
  bibdate =      "Tue Mar 14 18:08:54 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "https://arxiv.org/pdf/0708.3521.pdf",
  abstract =     "The arithmetic mean is the mean for addition and the
                 geometric mean is that for multiplication. Then what
                 kind of binary operation is associated with the
                 arithmetic--geometric mean (AGM) due to C. F. Gauss? If
                 it is possible to construct an arithmetic operation
                 such that AGM is the mean for this operation, it can be
                 regarded as an intermediate operation between addition
                 and multiplication in view of the meaning of AGM. In
                 this paper such an operation is introduced and several
                 of its algebraic properties are proved.",
  acknowledgement = ack-nhfb,
}

@Article{Walden:2007:HMI,
  author =       "Byron L. Walden and Lesley A. Ward",
  title =        "A harmonic measure interpretation of the
                 arithmetic--geometric mean",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "114",
  number =       "7",
  pages =        "610--622",
  year =         "2007",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "31A15 (26E60 28A12 30C20 30C85 33C45)",
  MRnumber =     "2341324",
  MRreviewer =   "Dimitrios Betsakos",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Bhatia:2008:MAG,
  author =       "Rajendra Bhatia and Fuad Kittaneh",
  title =        "The matrix arithmetic--geometric mean inequality
                 revisited",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "428",
  number =       "8--9",
  pages =        "2177--2191",
  day =          "15",
  month =        apr,
  year =         "2008",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2007.11.030",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A42 (47A30 47A63)",
  MRnumber =     "2401646",
  MRreviewer =   "Omar Hirzallah",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379507005381",
  abstract =     "Ideas related to matrix versions of the
                 arithmetic--geometric mean inequality are explained.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Matrix inequalities; Matrix monotone functions;
                 Pinching; Singular values; Unitarily invariant norms",
}

@Article{Carvalhaes:2008:APS,
  author =       "Claudio G. Carvalhaes and Patrick Suppes",
  title =        "Approximations for the period of the simple pendulum
                 based on the arithmetic--geometric mean",
  journal =      j-AMER-J-PHYSICS,
  volume =       "76",
  number =       "12",
  pages =        "1150--1154",
  month =        dec,
  year =         "2008",
  CODEN =        "AJPIAS",
  DOI =          "http://dx.doi.org/10.1119/1.2968864",
  ISSN =         "0002-9505 (print), 1943-2909 (electronic)",
  bibdate =      "Tue Mar 14 18:22:35 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  note =         "See comments in \cite{Villarino:2014:ASP} about prior
                 work before 1966 by Albert Edward Ingham (1900--1967)
                 producing both upper and lower bounds to approximations
                 to the period of a pendulum.",
  URL =          "http://aapt.scitation.org/doi/full/10.1119/1.2968864",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Physics",
  journal-URL =  "http://scitation.aip.org/content/aapt/journal/ajp",
  remark =       "From the introduction: ``The lack of an elementary
                 closed-form restricts the study of the simple pendulum
                 at the undergraduate level to small oscillations.
                 \ldots{} convergence with eight digits of accuracy is
                 obtained for an amplitude of $ 179^\circ $ after only
                 four iterations.''",
}

@Article{Feng:2008:MVS,
  author =       "Bao Qi Feng and Andrew Tonge",
  title =        "Matrix versions of some refinements of the
                 arithmetic--geometric mean inequality",
  journal =      j-J-MATH-SCI-ADV-APPL,
  volume =       "1",
  number =       "2",
  pages =        "243--264",
  year =         "2008",
  ISSN =         "0974-5750",
  MRclass =      "26E60 (15A45)",
  MRnumber =     "2530506",
  MRreviewer =   "Alan L. Horwitz",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Sciences. Advances and
                 Applications",
  journal-URL =  "http://www.scientificadvances.co.in/about-this-journal/1",
}

@Article{Jarvis:2008:HGA,
  author =       "Frazer Jarvis",
  title =        "Higher genus arithmetic--geometric means",
  journal =      j-RAMANUJAN-J,
  volume =       "17",
  number =       "1",
  pages =        "1--17",
  year =         "2008",
  CODEN =        "RAJOF9",
  DOI =          "http://dx.doi.org/10.1007/s11139-007-9058-0",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "14K25 (11B83 11F27)",
  MRnumber =     "2439522",
  MRreviewer =   "Cristiana Bertolin",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Ramanujan Journal. An International Journal Devoted to
                 the Areas of Mathematics Influenced by Ramanujan",
  journal-URL =  "http://link.springer.com/journal/11139",
}

@Article{Koike:2008:EGA,
  author =       "Kenji Koike and Hironori Shiga",
  title =        "An extended {Gauss} {AGM} and corresponding {Picard}
                 modular forms",
  journal =      j-J-NUMBER-THEORY,
  volume =       "128",
  number =       "7",
  pages =        "2097--2126",
  month =        jul,
  year =         "2008",
  CODEN =        "JNUTA9",
  DOI =          "http://dx.doi.org/10.1016/j.jnt.2007.12.001",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Tue Mar 14 17:07:32 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X08000218",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Lorentzen:2008:CDR,
  author =       "Lisa Lorentzen",
  title =        "Convergence and divergence of the {Ramanujan} {AGM}
                 fraction",
  journal =      j-RAMANUJAN-J,
  volume =       "16",
  number =       "1",
  pages =        "83--95",
  month =        may,
  year =         "2008",
  DOI =          "http://dx.doi.org/10.1007/s11139-007-9112-y",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  bibdate =      "Tue Mar 14 15:27:34 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  abstract =     "We prove that the Ramanujan AGM fraction diverges if $
                 |a| = |b| $ with $ a^2 \neq b^2 $. Thereby we prove two
                 conjectures posed by J. Borwein and R. Crandall. We
                 also demonstrate a method for accelerating the
                 convergence of this continued fraction when it
                 converges.",
  acknowledgement = ack-nhfb,
  fjournal =     "The {Ramanujan} Journal",
  journal-URL =  "http://link.springer.com/journal/11139",
}

@Article{Yeh:2008:SEF,
  author =       "Cheh-Chih Yeh and Hung-Wen Yeh and Wenyaw Chan",
  title =        "Some equivalent forms of the arithmetic--geometric
                 mean inequality in probability: a survey",
  journal =      j-J-INEQUAL-APPL,
  pages =        "Art. ID 386715, 9",
  year =         "2008",
  ISSN =         "1025-5834",
  MRclass =      "26E60 (60E15)",
  MRnumber =     "2449062",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Inequalities and Applications",
  journal-URL =  "http://journalofinequalitiesandapplications.springeropen.com/",
}

@Article{Cheon:2009:RBS,
  author =       "Gi-Sang Cheon and Andrew W. Eckford",
  title =        "A relationship between subpermanents and the
                 arithmetic--geometric mean inequality",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "430",
  number =       "1",
  pages =        "114--120",
  day =          "1",
  month =        jan,
  year =         "2009",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2008.07.001",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A15 (15A48)",
  MRnumber =     "2460503",
  MRreviewer =   "Carlos M. da Fonseca",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379508003406",
  abstract =     "Using the arithmetic--geometric mean inequality, we
                 give bounds for k-subpermanents of nonnegative $ n
                 \times n $ matrices $F$. In the case $ k = n$, we
                 exhibit an $ n^2$-set $S$ whose arithmetic and
                 geometric means constitute upper and lower bounds for $
                 \per (F) / n!$. We offer sharpened versions of these
                 bounds when $F$ has zero-valued entries.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "AM--GM inequality; Permanent; Subpermanent",
}

@Article{Furuichi:2009:TIP,
  author =       "Shigeru Furuichi and Ken Kuriyama and Kenjiro Yanagi",
  title =        "Trace inequalities for products of matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "430",
  number =       "8--9",
  pages =        "2271--2276",
  year =         "2009",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2008.12.003",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379508005685",
  abstract =     "In this short paper, we study some trace inequalities
                 of the products of the matrices and the power of
                 matrices by the use of elementary calculations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric mean inequality and nonnegative
                 matrix; Matrix trace inequalitiy",
}

@Article{Hayashi:2009:NCA,
  author =       "Tomohiro Hayashi",
  title =        "Non-commutative arithmetic--geometric mean
                 inequality",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "137",
  number =       "10",
  pages =        "3399--3406",
  year =         "2009",
  CODEN =        "PAMYAR",
  DOI =          "http://dx.doi.org/10.1090/S0002-9939-09-09911-0",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "47A63",
  MRnumber =     "2515409",
  MRreviewer =   "{\`E}dward L. Pekarev",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Kosheleva:2009:GNJ,
  author =       "O. Kosheleva and V. Kreinovich",
  title =        "Guesstimation: a New Justification of the Geometric
                 Mean Heuristic",
  journal =      j-APPL-MATH-SCI-RUSE,
  volume =       "3",
  number =       "47",
  pages =        "2335--2342",
  year =         "2009",
  ISSN =         "1312-885x (print), 1314-7552 (electronic)",
  MRclass =      "62F10",
  MRnumber =     "MR2558236 (2010i:62055)",
  bibdate =      "Fri Oct 15 09:08:58 2010",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.cs.utep.edu/vladik/2009/tr09-10.pdf;
                 http://www.openj-gate.com/Browse/ArticleList.aspx?Journal_id=124136&issue_id=1153557",
  abstract =     "In many practical situations in which the only
                 information we have about the quantity $x$ is that its
                 value is within an interval $ [\underbar {x}; \overbar
                 {x}]$, a responsible estimate for this quantity is the
                 geometric mean of the bounds $ \sqrt {\underbar {x}
                 \cdot \overbar {x}}$. In this paper, we provide a new
                 justification for this geometric mean heuristic.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematical Sciences (Ruse)",
  journal-URL =  "http://www.m-hikari.com/ams/",
  keywords =     "arithmetic mean; geometric mean; interval arithmetic",
}

@Article{Lekner:2009:ASC,
  author =       "John Lekner",
  title =        "Axially symmetric charge distributions and the
                 arithmetic--geometric mean",
  journal =      j-J-ELECTROST,
  volume =       "67",
  number =       "6",
  pages =        "880--885",
  year =         "2009",
  CODEN =        "JOELDH",
  DOI =          "http://dx.doi.org/10.1016/j.elstat.2009.07.007",
  ISSN =         "0304-3886 (print), 1873-5738 (electronic)",
  ISSN-L =       "0304-3886",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0304388609001806",
  abstract =     "The potential at an arbitrary point in space due to an
                 axially symmetric charge distribution is related to the
                 arithmetic--geometric mean of the maximum and minimum
                 distances from each annulus of constant charge density.
                 The arithmetic--geometric mean is expressible in terms
                 of the elliptic integral of the first kind, $K$. Thus
                 the potential of a charged body with cylindrical
                 symmetry is reducible to a double integral over the
                 charge density times $K$. For conductors the charge
                 resides on the surface, and the potential reduces to a
                 single integral over the surface charge density times
                 $K$. This result leads to a new proof of the relation
                 between a sum over products of Legendre polynomials and
                 the complete elliptic integral of the first kind, and
                 to new identities for the angular average of Legendre
                 polynomials divided by $ | r - r' |$. The method also
                 provides a direct route to the capacitance of a slender
                 torus, without the use of toroidal coordinates.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Electrost.",
  fjournal =     "Journal of Electrostatics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043886",
  keywords =     "Arithmetic--geometric mean; Axially symmetric charge
                 distributions; Thin torus",
}

@Article{Qi:2009:AUP,
  author =       "Feng Qi and Anthony Sofo",
  title =        "An alternative and united proof of a double inequality
                 for bounding the arithmetic--geometric mean",
  journal =      "Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl.
                 Math. Phys.",
  volume =       "71",
  number =       "3",
  pages =        "69--76",
  year =         "2009",
  ISSN =         "1223-7027",
  MRclass =      "26E60 (26D15)",
  MRnumber =     "2553929",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "``Politehnica'' University of Bucharest. Scientific
                 Bulletin. Series A. Applied Mathematics and Physics",
}

@InCollection{Arndt:2010:AEI,
  author =       "J{\"o}rg Arndt",
  title =        "The {AGM}, elliptic integrals, and algorithms for
                 computing $ \pi $",
  crossref =     "Arndt:2011:MC",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "599--621",
  year =         "2011",
  DOI =          "http://dx.doi.org/10.1007/978-3-642-14764-7_31",
  bibdate =      "Tue Mar 14 15:06:12 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Unpublished{Brent:2010:MPZ,
  author =       "Richard P. Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  day =          "20",
  month =        apr,
  year =         "2010",
  MRclass =      "11Y60 (Primary), 65Y20 (Secondary)",
  bibdate =      "Tue Apr 26 14:13:36 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib",
  note =         "Reprint of \cite{Brent:1976:MPZ} with a postscript
                 describing more recent developments. See also
                 \cite{Salamin:1976:CUA}",
  URL =          "http://arxiv.org/abs/1004.3412v2;
                 http://wwwmaths.anu.edu.au/~brent/pub/pub028.html",
  abstract =     "We consider methods for finding high-precision
                 approximations to simple zeros of smooth functions. As
                 an application, we give fast methods for evaluating the
                 elementary functions $ \log (x) $, $ \exp (x) $, $ \sin
                 (x) $ etc. to high precision. For example, if $x$ is a
                 positive floating-point number with an $n$-bit
                 fraction, then (under rather weak assumptions) an
                 $n$-bit approximation to $ \log (x)$ or $ \exp (x)$ may
                 be computed in time asymptotically equal to $ 13 M(n)
                 \lg (n)$, where $ M(n)$ is the time required to
                 multiply floating-point numbers with $n$-bit fractions.
                 Similar results are given for the other elementary
                 functions. Some analogies with operations on formal
                 power series (over a field of characteristic zero) are
                 discussed. In particular, it is possible to compute the
                 first $n$ terms in $ \log (1 + a_1 x + \cdots)$ or $
                 \exp (a_1. x) + \cdots $ in time $ O(M(n))$, where $
                 M(n)$ is the time required to multiply two polynomials
                 of degree $ n - 1$. It follows that the first $n$ terms
                 in a $q$-th power $ (1 + a_1 x + \cdots)^q$ can be
                 computed in time $ O(M(n))$, independent of $q$. One of
                 the results of this paper is the ``Gauss--Legendre'' or
                 ``Brent--Salamin'' algorithm for computing pi. This is
                 the first quadratically convergent algorithm for pi. It
                 was also published in Brent [J. ACM 23 (1976),
                 242--251], and independently by Salamin [Math. Comp. 30
                 (1976), 565--570].",
  acknowledgement = ack-nhfb,
}

@Article{Brent:2010:UAE,
  author =       "Richard P. Brent",
  title =        "Unrestricted algorithms for elementary and special
                 functions",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--13",
  month =        apr,
  year =         "2010",
  bibdate =      "Sat Feb 25 10:56:45 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://arxiv.org/abs/1004.3621",
  abstract =     "We describe some ``unrestricted'' algorithms which are
                 useful for the computation of elementary and special
                 functions when the precision required is not known in
                 advance. Several general classes of algorithms are
                 identified and illustrated by examples. The topics
                 include: power series methods, use of halving
                 identities, asymptotic expansions, continued fractions,
                 recurrence relations, Newton's method, numerical
                 contour integration, and the arithmetic--geometric
                 mean. Most of the algorithms discussed are implemented
                 in the MP package.",
  acknowledgement = ack-nhfb,
}

@Article{Cardenas-Barron:2010:EMD,
  author =       "Leopoldo Eduardo C{\'a}rdenas-Barr{\'o}n",
  title =        "An easy method to derive {EOQ} and {EPQ} inventory
                 models with backorders",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "59",
  number =       "2",
  pages =        "948--952",
  year =         "2010",
  CODEN =        "CMAPDK",
  DOI =          "http://dx.doi.org/10.1016/j.camwa.2009.09.013",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122109006774",
  abstract =     "Recently, a cost minimization method to determine the
                 lot size for the EOQ/EPQ models with backorders was
                 published. This method is based on the well-known
                 arithmetic--geometric mean inequality. Although the
                 cost minimization method is correct and interesting, it
                 does not focus on deriving the backorders level. This
                 paper proposes another simple approach. The proposed
                 method finds both the lot size and the backorders
                 level.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Algebraic optimization; Arithmetic--geometric mean
                 (AGM) inequality; Backorders level;
                 Cauchy--Bunyakovsky--Schwarz (CBS) inequality; Cost
                 comparisons optimization; Economic order quantity;
                 Economic production quantity",
}

@Article{Cardenas-Barron:2010:SMC,
  author =       "Leopoldo Eduardo C{\'a}rdenas-Barr{\'o}n",
  title =        "A simple method to compute economic order quantities:
                 Some observations",
  journal =      j-APPL-MATH-MODEL,
  volume =       "34",
  number =       "6",
  pages =        "1684--1688",
  year =         "2010",
  CODEN =        "AMMODL",
  DOI =          "http://dx.doi.org/10.1016/j.apm.2009.08.024",
  ISSN =         "0307-904x (print), 1872-8480 (electronic)",
  ISSN-L =       "0307-904X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0307904X09002777",
  abstract =     "Teng [2] presents an arithmetic--geometric mean method
                 to be applied to determine the optimal lot size for the
                 EOQ/EPQ models, taking into account backorders.
                 Although the arithmetic--geometric mean method is
                 correct, arguments as to when (not) to use the
                 arithmetic--geometric mean inequality as optimization
                 method are not complete. Moreover, this optimization
                 method does not focus on the method for deriving the
                 optimal backorders level. The main purpose of this work
                 is to overcome these shortcomings, presents a
                 discussion of when (not) to use the cost minimization
                 method and derives the optimal backorders level.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied mathematical modelling",
  keywords =     "Algebraic optimization; Arithmetic--geometric mean
                 optimization; Backorders; Cost comparisons
                 optimization; Cost-difference comparisons optimization;
                 EOQ/EPQ",
}

@Article{Kinjo:2010:AAG,
  author =       "Kensaku Kinjo and Yuken Miyasaka",
  title =        "$2$-{Adic} arithmetic--geometric mean and elliptic
                 curves",
  journal =      j-INTERDISCIP-INFORM-SCI,
  volume =       "16",
  number =       "1",
  pages =        "5--15",
  year =         "2010",
  DOI =          "http://dx.doi.org/10.4036/iis.2010.5",
  ISSN =         "1340-9050 (print), 1347-6157 (electronic)",
  ISSN-L =       "1340-9050",
  MRclass =      "11S85 (11G07)",
  MRnumber =     "2648110",
  MRreviewer =   "Maria Sabitova",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Interdisciplinary Information Sciences",
  journal-URL =  "https://www.jstage.jst.go.jp/browse/iis",
}

@Article{Matsumoto:2010:AGM,
  author =       "Keiji Matsumoto and Tomohide Terasoma",
  title =        "Arithmetic--geometric means for hyperelliptic curves
                 and {Calabi--Yau} varieties",
  journal =      j-INT-J-MATH,
  volume =       "21",
  number =       "7",
  pages =        "939--949",
  year =         "2010",
  DOI =          "http://dx.doi.org/10.1142/S0129167X1000632X",
  ISSN =         "0129-167X",
  MRclass =      "14K20 (14J32 14K25)",
  MRnumber =     "2671531",
  MRreviewer =   "Ahmed Lesfari",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijm",
}

@Article{Bayat:2011:AGM,
  author =       "M. Bayat and H. Teimoori",
  title =        "{Arithmetic--Geometric Mean} determinantal identity",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "435",
  number =       "11",
  pages =        "2936--2941",
  day =          "1",
  month =        dec,
  year =         "2011",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2011.05.031",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A24 (15A15)",
  MRnumber =     "2825293",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S002437951100440X",
  abstract =     "In this paper, we give a generalization of a
                 determinantal identity posed by Charles R. Johnson
                 about minors of a Toeplitz matrix satisfying a specific
                 matrix identity. These minors are those appear in the
                 Dodgson's condensation formula.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
  keywords =     "AGM (arithmetic--geometric mean);
                 Arithmetic--Geometric Mean; Determinantal identity;
                 Dodgson's condensation; Toeplitz matrix",
}

@Article{Chu:2011:OIB,
  author =       "Yu-Ming Chu and Miao-Kun Wang",
  title =        "Optimal inequalities between harmonic, geometric,
                 logarithmic, and arithmetic--geometric means",
  journal =      j-J-APPL-MATH,
  pages =        "Art. ID 618929, 9",
  year =         "2011",
  DOI =          "http://dx.doi.org/10.1155/2011/618929",
  ISSN =         "1110-757x (print), 1687-0042 (electronic)",
  ISSN-L =       "1110-757X",
  MRclass =      "26E60",
  MRnumber =     "2846444",
  MRreviewer =   "Raghib M. Abu-Saris",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Mathematics",
  journal-URL =  "http://www.hindawi.com/journals/jam/",
}

@Article{Dupont:2011:FEM,
  author =       "R{\'e}gis Dupont",
  title =        "Fast evaluation of modular functions using {Newton}
                 iterations and the {AGM}",
  journal =      j-MATH-COMPUT,
  volume =       "80",
  number =       "275",
  pages =        "1823--1847",
  month =        jul,
  year =         "2011",
  CODEN =        "MCMPAF",
  DOI =          "http://dx.doi.org/10.1090/S0025-5718-2011-01880-6",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Apr 18 06:32:30 MDT 2011",
  bibsource =    "http://www.ams.org/mcom/2011-80-275;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-01880-6/;
                 http://www.ams.org/journals/mcom/2011-80-275/S0025-5718-2011-01880-6/S0025-5718-2011-01880-6.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Gauss:2011:W,
  author =       "Carl Friedrich Gauss",
  title =        "Werke",
  volume =       "3",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "514",
  year =         "2011",
  DOI =          "http://dx.doi.org/10.1017/CBO9781139058247",
  ISBN =         "1-108-03225-7 (paperback), 1-139-05824-X (e-book)",
  ISBN-13 =      "978-1-108-03225-4 (paperback), 978-1-139-05824-7
                 (e-book)",
  LCCN =         "????",
  bibdate =      "Tue Mar 14 18:59:37 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Cambridge library collection. Mathematics",
  abstract =     "The genius of Carl Friedrich Gauss (1777-1855) and the
                 novelty of his work (published in Latin, German, and
                 occasionally French) in areas as diverse as number
                 theory, probability and astronomy were already widely
                 acknowledged during his lifetime. But it took another
                 three generations of mathematicians to reveal the true
                 extent of his output as they studied Gauss' extensive
                 unpublished papers and his voluminous correspondence.
                 This posthumous twelve-volume collection of Gauss'
                 complete works, published between 1863 and 1933, marks
                 the culmination of their efforts and provides a
                 fascinating account of one of the great scientific
                 minds of the nineteenth century. Volume 3, which
                 appeared in 1866, focuses on analysis. It includes
                 Gauss' work on elliptic functions and on power series,
                 for which he gave the first convergence criteria, as
                 well as his first (1799) proof of the fundamental
                 theorem of algebra, and reviews of works by
                 contemporaries including Fourier.",
  acknowledgement = ack-nhfb,
  author-dates = "1777--1855",
  remark =       "Originally published in G{\"o}ttingen: Koniglichen
                 Gesellschaft der Wissenschaften, 1866",
}

@Article{Kim:2011:MGM,
  author =       "Sejong Kim and Jimmie Lawson and Yongdo Lim",
  title =        "The matrix geometric mean of parameterized, weighted
                 arithmetic and harmonic means",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "435",
  number =       "9",
  pages =        "2114--2131",
  day =          "1",
  month =        nov,
  year =         "2011",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Mon Jun 13 18:34:49 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.sciencedirect.com/science/journal/00243795",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Shirali:2011:BPG,
  author =       "Shailesh A. Shirali",
  title =        "95.09 {A} bootstrapping proof of the {AM--GM}
                 Inequality for three variables",
  journal =      j-MATH-GAZ,
  volume =       "95",
  number =       "532",
  pages =        "86--87",
  month =        mar,
  year =         "2011",
  CODEN =        "MAGAAS",
  DOI =          "http://dx.doi.org/10.1017/S0025557200002412",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue May 5 12:04:14 MDT 2015",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=MAG&volumeId=95&issueId=532;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayBackIssues?jid=MAG",
}

@Article{Wang:2011:SDI,
  author =       "Miao-Kun Wang and Yu-Ming Chu and Gen-Di Wang",
  title =        "A Sharp Double Inequality Between the {Lehmer} and
                 Arithmetic--Geometric Means",
  journal =      j-PAC-J-APPL-MATH,
  volume =       "3",
  number =       "4",
  pages =        "281--286",
  month =        "????",
  year =         "2011",
  ISSN =         "1941-3963",
  MRclass =      "26E60",
  MRnumber =     "3024759",
  bibdate =      "Wed Mar 15 07:14:39 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "https://www.novapublishers.com/catalog/product_info.php?products_id=24770",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Applied Mathematics",
  journal-URL =  "http://www.novapublishers.com/catalog/product_info.php?products_id=6697",
}

@Article{Albadawi:2012:SVA,
  author =       "Hussien Albadawi",
  title =        "Singular value and arithmetic--geometric mean
                 inequalities for operators",
  journal =      j-ANN-FUNCT-ANAL,
  volume =       "3",
  number =       "1",
  pages =        "10--18",
  year =         "2012",
  DOI =          "http://dx.doi.org/10.15352/afa/1399900020",
  ISSN =         "2008-8752",
  MRclass =      "47A30",
  MRnumber =     "2903264",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Functional Analysis",
  journal-URL =  "http://projecteuclid.org/afa",
}

@Article{Barratt:2012:IPC,
  author =       "Carl Barratt and Ramesh Sharma",
  title =        "96.16 {An} inductive proof of the condition for the
                 {AM--GM} equality",
  journal =      j-MATH-GAZ,
  volume =       "96",
  number =       "535",
  pages =        "131--133",
  month =        mar,
  year =         "2012",
  CODEN =        "MAGAAS",
  DOI =          "http://dx.doi.org/10.1017/S0025557200004162",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue May 5 12:04:21 MDT 2015",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=MAG&volumeId=96&issueId=535;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayBackIssues?jid=MAG",
}

@Article{Chung:2012:VAG,
  author =       "Kun-Jen Chung",
  title =        "On the validity of the arithmetic--geometric mean
                 method to locate the optimal solution in a supply chain
                 system",
  journal =      j-INT-J-SYST-SCI,
  volume =       "43",
  number =       "8",
  pages =        "1454--1463",
  year =         "2012",
  CODEN =        "IJSYA9",
  DOI =          "http://dx.doi.org/10.1080/00207721.2010.547628",
  ISSN =         "0020-7721 (print), 1464-5319 (electronic)",
  ISSN-L =       "0020-7721",
  MRclass =      "90B05",
  MRnumber =     "2946981",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Systems Science. Principles
                 and Applications of Systems and Integration",
  journal-URL =  "http://www.tandfonline.com/loi/tsys20",
}

@Article{Hadjidimos:2012:IEO,
  author =       "Apostolos Hadjidimos",
  title =        "Irreducibility and extensions of {Ostrowski's
                 Theorem}",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "436",
  number =       "7",
  pages =        "2156--2168",
  year =         "2012",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2011.11.035",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379511007786",
  abstract =     "In this paper an extension of Ostrowski's Theorem for
                 complex square irreducible matrices is presented. Also
                 extensions of similar statements for square complex
                 matrices are analyzed and completed. Most of the
                 statements in this work cover also the case of
                 reducible matrices.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Alpha-matrices; Ostrowski's Theorems; H{\"o}lder
                 inequality; (irreducibly) diagonally dominant matrices;
                 Generalized arithmetic--geometric mean inequality",
}

@Article{He:2012:IAG,
  author =       "Chuanjiang He and Limin Zou and Shahid Qaisar",
  title =        "On improved arithmetic--geometric mean and {Heinz}
                 inequalities for matrices",
  journal =      j-J-MATH-INEQUAL,
  volume =       "6",
  number =       "3",
  pages =        "453--459",
  year =         "2012",
  DOI =          "http://dx.doi.org/10.7153/jmi-06-42",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "15A42 (15A18 15A60)",
  MRnumber =     "3012207",
  MRreviewer =   "Jaspal Singh Aujla",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Kinjo:2012:HSA,
  author =       "Kensaku Kinjo and Yuken Miyasaka",
  title =        "Hypergeometric series and arithmetic--geometric mean
                 over 2-adic fields",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "8",
  number =       "3",
  pages =        "831--844",
  year =         "2012",
  DOI =          "http://dx.doi.org/10.1142/S1793042112500480",
  ISSN =         "1793-0421 (print), 1933-8368 (electronic)",
  MRclass =      "11S80 (11G20 33C05)",
  MRnumber =     "2904934",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Maligranda:2012:GIE,
  author =       "Lech Maligranda",
  title =        "The {AM--GM} Inequality is Equivalent to the
                 {Bernoulli} Inequality",
  journal =      j-MATH-INTEL,
  volume =       "34",
  number =       "1",
  pages =        "1--2",
  month =        "????",
  year =         "2012",
  CODEN =        "MAINDC",
  DOI =          "http://dx.doi.org/10.1007/s00283-011-9266-8",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  bibdate =      "Thu Feb 14 06:39:03 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
  keywords =     "AM (arithmetic mean); GM (geometric mean)",
  remark =       "This paper references two books that provide 52 and 74
                 proofs of the {\em Cauchy inequality\/} (1821), {$ {\rm
                 AM} \geq {\rm GM} $}, and gives a short proof that it
                 and the {\em Barrow--Bernoulli inequality} (1670,
                 1689), $ x^n \geq 1 + n(x - 1) $, for any $ x > 0 $ and
                 $n$ an integer, are mutually equivalent: either one
                 implies the other.",
}

@Article{Seo:2012:AGM,
  author =       "Yuki Seo",
  title =        "The arithmetic--geometric mean inequality in an
                 external formula",
  journal =      j-SCI-MATH-JPN,
  volume =       "75",
  number =       "3",
  pages =        "299--305",
  year =         "2012",
  ISSN =         "1346-0862",
  ISSN-L =       "1346-0447",
  MRclass =      "47A63 (26D10)",
  MRnumber =     "3099760",
  MRreviewer =   "T. Ando",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientiae Mathematicae Japonicae",
  journal-URL =  "http://www.jams.or.jp/notice/scmj/smj.html",
}

@Article{Spandaw:2012:HIG,
  author =       "Jeroen Spandaw and Duco van Straten",
  title =        "Hyperelliptic integrals and generalized
                 arithmetic--geometric mean",
  journal =      j-RAMANUJAN-J,
  volume =       "28",
  number =       "1",
  pages =        "61--78",
  year =         "2012",
  CODEN =        "RAJOF9",
  DOI =          "http://dx.doi.org/10.1007/s11139-011-9353-7",
  ISSN =         "1382-4090 (print), 1572-9303 (electronic)",
  ISSN-L =       "1382-4090",
  MRclass =      "14K25 (14H40)",
  MRnumber =     "2914453",
  MRreviewer =   "Ahmed Lesfari",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Ramanujan Journal. An International Journal Devoted to
                 the Areas of Mathematics Influenced by Ramanujan",
  journal-URL =  "http://link.springer.com/journal/11139",
}

@Article{Wang:2012:SDI,
  author =       "Miao-Kun Wang and Yu-Ming Chu and Gen-Di Wang",
  title =        "A Sharp Double Inequality Between the {Lehmer} and
                 Arithmetic--Geometric Means",
  journal =      j-PAC-J-APPL-MATH,
  volume =       "4",
  number =       "1",
  pages =        "1--25",
  year =         "2012",
  ISSN =         "1941-3963",
  MRclass =      "26E60 (26D07)",
  MRnumber =     "3027346",
  bibdate =      "Wed Mar 15 07:16:27 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Applied Mathematics",
  journal-URL =  "http://www.novapublishers.com/catalog/product_info.php?products_id=6697",
}

@Article{Baricz:2013:TTI,
  author =       "{\'A}rp{\'a}d Baricz and Kondooru Raghavendar and
                 Anbhu Swaminathan",
  title =        "{Tur{\'a}n} type inequalities for $q$-hypergeometric
                 functions",
  journal =      j-J-APPROX-THEORY,
  volume =       "168",
  number =       "??",
  pages =        "69--79",
  year =         "2013",
  CODEN =        "JAXTAZ",
  DOI =          "http://dx.doi.org/10.1016/j.jat.2013.01.002",
  ISSN =         "0021-9045 (print), 1096-0430 (electronic)",
  ISSN-L =       "0021-9045",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021904513000129",
  abstract =     "In this paper our aim is to deduce some Tur{\'a}n type
                 inequalities for $q$-hypergeometric and $q$-confluent
                 hypergeometric functions. In order to obtain the main
                 results we apply the methods developed in the case of
                 classical Kummer and Gauss hypergeometric functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  keywords =     "Arithmetic, geometric mean; Basic hypergeometric
                 functions; Gauss and Kummer hypergeometric functions; q
                 -Kummer confluent hypergeometric functions; Tur{\'a}n
                 type inequalities",
}

@Article{Chu:2013:STP,
  author =       "Yu-Ming Chu and Miao-Kun Wang and Ye-Fang Qiu and
                 Xiao-Yan Ma",
  title =        "Sharp two parameter bounds for the logarithmic mean
                 and the arithmetic--geometric mean of {Gauss}",
  journal =      j-J-MATH-INEQUAL,
  volume =       "7",
  number =       "3",
  pages =        "349--355",
  year =         "2013",
  DOI =          "http://dx.doi.org/10.7153/jmi-07-31",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "26E60",
  MRnumber =     "3115070",
  MRreviewer =   "Biljana P. Mihailovi{\'c}",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Cremona:2013:CAPa,
  author =       "John E. Cremona and Thotsaphon Thongjunthug",
  title =        "The complex {AGM}, periods of elliptic curves over and
                 complex elliptic logarithms",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--32",
  day =          "20",
  month =        feb,
  year =         "2013",
  bibdate =      "Tue Mar 14 18:14:33 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "https://arxiv.org/pdf/1011.0914.pdf",
  abstract =     "We give an account of the complex
                 Arithmetic--Geometric Mean (AGM), as first studied by
                 Gauss, together with details of its relationship with
                 the theory of elliptic curves over $C$, their period
                 lattices and complex parametrisation. As an
                 application, we present efficient methods for computing
                 bases for the period lattices and elliptic logarithms
                 of points, for arbitrary elliptic curves defined over
                 $C$. Earlier authors have only treated the case of
                 elliptic curves defined over the real numbers; here,
                 the multi-valued nature of the complex AGM plays an
                 important role. Our method, which we have implemented
                 in both MAGMA and Sage, is illustrated with several
                 examples using elliptic curves defined over number
                 fields with real and complex embeddings.",
  acknowledgement = ack-nhfb,
}

@Article{Cremona:2013:CAPb,
  author =       "John E. Cremona and Thotsaphon Thongjunthug",
  title =        "The complex {AGM}, periods of elliptic curves over and
                 complex elliptic logarithms",
  journal =      j-J-NUMBER-THEORY,
  volume =       "133",
  number =       "8",
  pages =        "2813--2841",
  year =         "2013",
  CODEN =        "JNUTA9",
  DOI =          "http://dx.doi.org/10.1016/j.jnt.2013.02.002",
  ISSN =         "0022-314x (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X13000735",
  abstract =     "We give an account of the complex
                 Arithmetic--Geometric Mean (AGM), as first studied by
                 Gauss, together with details of its relationship with
                 the theory of elliptic curves over $C$, their period
                 lattices and complex parametrisation. As an
                 application, we present efficient methods for computing
                 bases for the period lattices and elliptic logarithms
                 of points, for arbitrary elliptic curves defined over
                 $C$. Earlier authors have only treated the case of
                 elliptic curves defined over the real numbers; here,
                 the multi-valued nature of the complex AGM plays an
                 important role. Our method, which we have implemented
                 in both MAGMA and Sage, is illustrated with several
                 examples using elliptic curves defined over number
                 fields with real and complex embeddings.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
  keywords =     "Arithmetic--geometric mean; Elliptic curve; Elliptic
                 logarithm; Period lattice",
}

@Article{Crisan:2013:DSI,
  author =       "O. Crisan and S. Kanas",
  title =        "Differential subordinations involving arithmetic and
                 geometric means",
  journal =      j-APPL-MATH-COMP,
  volume =       "222",
  number =       "??",
  pages =        "123--131",
  day =          "1",
  month =        oct,
  year =         "2013",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Dec 2 12:34:37 MST 2013",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300313008011",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Gumus:2013:IAG,
  author =       "I. Halil Gumus and Necati Taskara",
  title =        "The improved arithmetic--geometric mean inequalities
                 for matrix norms",
  journal =      j-APPL-MATH-SCI-RUSE,
  volume =       "7",
  number =       "29--32",
  pages =        "1439--1446",
  year =         "2013",
  DOI =          "http://dx.doi.org/10.12988/ams.2013.13132",
  ISSN =         "1312-885x (print), 1314-7552 (electronic)",
  MRclass =      "26D15",
  MRnumber =     "3021302",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematical Sciences",
  journal-URL =  "http://www.m-hikari.com/ams/",
}

@Article{Hassani:2013:AGM,
  author =       "Mehdi Hassani",
  title =        "On the arithmetic--geometric mean inequality",
  journal =      j-TAMKANG-J-MATH,
  volume =       "44",
  number =       "4",
  pages =        "453--456",
  year =         "2013",
  DOI =          "http://dx.doi.org/10.5556/j.tkjm.44.2013.1418",
  ISSN =         "0049-2930 (print), 2073-9826 (electronic)",
  ISSN-L =       "2073-9826",
  MRclass =      "26D15",
  MRnumber =     "3153080",
  MRreviewer =   "M. E. Muldoon",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tamkang Journal of Mathematics",
  journal-URL =  "http://journals.math.tku.edu.tw/index.php/TKJM",
}

@InCollection{Kinjo:2013:HSA,
  author =       "Kensaku Kinjo and Yuken Miyasaka",
  booktitle =    "Algebraic number theory and related topics 2011",
  title =        "Hypergeometric series and arithmetic--geometric mean
                 over 2-adic fields",
  publisher =    "Res. Inst. Math. Sci. (RIMS), Kyoto",
  pages =        "99--110",
  year =         "2013",
  MRclass =      "11G20 (33C05)",
  MRnumber =     "3221722",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "RIMS K\^oky\^uroku Bessatsu, B44",
  acknowledgement = ack-nhfb,
}

@Article{Najafi:2013:SRK,
  author =       "Hamed Najafi",
  title =        "Some results on {Kwong} functions and related
                 inequalities",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "439",
  number =       "9",
  pages =        "2634--2641",
  year =         "2013",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2013.06.018",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379513004175",
  abstract =     "We investigate some relations between Kwong functions
                 and operator monotone functions. As an application, we
                 present an arithmetic--geometric mean type inequality
                 by showing that for two continuous functions $f$, $g$
                 on $ (0, \infty)$ such that $ h (t) = f (t) g (t)$ is a
                 Kwong function and $ f (t) g (t) \leq t$, any positive
                 matrices $A$, $B$ and any matrix $X$, it holds that $
                 ||| f (A) X g (B) + g (A) X f (B) ||| \leq ||| A X + X
                 B |||$ for each unitarily invariant norm $ ||| \cdot
                 |||$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Arithmetic--geometric mean type inequality; Kwong
                 function; Operator monotone function",
}

@Article{Ouyang:2013:OPL,
  author =       "Liang-Yuh Ouyang and Chun-Tao Chang",
  title =        "Optimal production lot with imperfect production
                 process under permissible delay in payments and
                 complete backlogging",
  journal =      j-INT-J-PROD-ECON,
  volume =       "144",
  number =       "2",
  pages =        "610--617",
  year =         "2013",
  CODEN =        "JPCEYE",
  DOI =          "http://dx.doi.org/10.1016/j.ijpe.2013.04.027",
  ISSN =         "0925-5273 (print), 1873-7579 (electronic)",
  ISSN-L =       "0925-5273",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0925527313001916",
  abstract =     "The traditional economic production quantity (EPQ)
                 model assumes that the production products are all
                 perfect. It is not always true in the real production
                 system, due to imperfect production process or other
                 factors, imperfect quality items may be produced.
                 Furthermore, it is well-known that the total
                 production-inventory costs can be reduced by reworking
                 the imperfect quality items produced with a relatively
                 smaller additional reworking and holding costs. In
                 addition, the permissible delay in payments offered by
                 the supplier is widely adopted in the practical
                 business market. In this study, we explore the effects
                 of the reworking imperfect quality items and trade
                 credit on the EPQ model with imperfect production
                 processes and complete backlogging. A mathematical
                 model which includes the reworking and shortage costs,
                 interest earned and interest charged is presented.
                 Besides, an arithmetic--geometric mean inequality
                 approach is employed and an algorithm is developed to
                 find the optimal production policy. Furthermore, some
                 numerical examples and sensitivity analysis are
                 provided to demonstrate the proposed model.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Production Economics",
  keywords =     "Arithmetic--geometric mean inequality; Complete
                 backlogging; Imperfect production process; Inventory;
                 Permissible delay in payments",
}

@Article{Xu:2013:PPM,
  author =       "Bai-Xiang Xu and Yang Gao and Min-Zhong Wang",
  title =        "Particle packing and the mean theory",
  journal =      j-PHYS-LET-A,
  volume =       "377",
  number =       "3--4",
  pages =        "145--147",
  year =         "2013",
  CODEN =        "PYLAAG",
  DOI =          "http://dx.doi.org/10.1016/j.physleta.2012.11.022",
  ISSN =         "0375-9601 (print), 1873-2429 (electronic)",
  ISSN-L =       "0375-9601",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/kepler.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0375960112011772",
  abstract =     "This Letter presents two mean relations between the
                 densities/porosities of random and regular packing
                 modes. The two mean relations work very well for the
                 packing of spherical particles, cubic particles and
                 circular discs. Results confirm the corresponding
                 experimental and computational results.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03759601",
  keywords =     "Arithmetic--geometric mean; Harmonic--geometric mean;
                 Packing density; Particle packing",
}

@Article{Yamazaki:2013:EPA,
  author =       "T. Yamazaki",
  title =        "An elementary proof of arithmetic--geometric mean
                 inequality of the weighted {Riemannian} mean of
                 positive definite matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "438",
  number =       "4",
  pages =        "1564--1569",
  day =          "15",
  month =        feb,
  year =         "2013",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2011.12.006",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15B48",
  MRnumber =     "3005242",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala2010.bib",
  note =         "16th \{ILAS\} Conference Proceedings, Pisa 2010",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379511007865",
  abstract =     "The weighted Riemannian mean of positive definite
                 matrices is a kind of weighted geometric mean of n
                 matrices. Some properties of the weighted Riemannian
                 mean are easily obtained. But some of them are not
                 easy. In this short paper, a simplified proof of
                 arithmetic--geometric--harmonic mean inequalities will
                 be obtained.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
  keywords =     "Arithmetic--geometric mean inequality; Geometric mean;
                 Matrix inequality; Positive definite matrix; The
                 Riemannian mean",
}

@Article{Chang:2014:API,
  author =       "Hung-Chi Chang",
  title =        "An analysis of production-inventory models with
                 deteriorating items in a two-echelon supply chain",
  journal =      j-APPL-MATH-MODEL,
  volume =       "38",
  number =       "3",
  pages =        "1187--1191",
  year =         "2014",
  CODEN =        "AMMODL",
  DOI =          "http://dx.doi.org/10.1016/j.apm.2013.07.031",
  ISSN =         "0307-904x (print), 1872-8480 (electronic)",
  ISSN-L =       "0307-904X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0307904X13004757",
  abstract =     "This paper revisits two previous studies that
                 addressed the integrated production--inventory problem
                 for deteriorating items in a two-echelon supply chain,
                 where the item's deterioration rate is a constant or
                 follows a continuous probability distribution function.
                 The aim of this study is to present an improved
                 solution procedure to determine the delivery lot size
                 and the number of deliveries per production batch cycle
                 that minimizes the total cost of the entire supply
                 chain. The performance of the proposed methodology is
                 illustrated analytically and numerically.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied mathematical modelling",
  keywords =     "Arithmetic--geometric mean method; Inventory; Marginal
                 analysis; Probabilistic deterioration; Supply chain",
}

@Article{Hassani:2014:AGM,
  author =       "Mehdi Hassani",
  title =        "On the arithmetic--geometric means of positive
                 integers and the number $e$",
  journal =      "Appl. Math. E-Notes",
  volume =       "14",
  pages =        "250--255",
  year =         "2014",
  ISSN =         "1607-2510",
  MRclass =      "26E60",
  MRnumber =     "3324424",
  MRreviewer =   "Bing Xu",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics E-Notes",
}

@Article{Jameson:2014:AAG,
  author =       "G. J. O. Jameson",
  title =        "An approximation to the arithmetic--geometric mean",
  journal =      j-MATH-GAZ,
  volume =       "98",
  number =       "541",
  pages =        "85--95",
  month =        mar,
  year =         "2014",
  CODEN =        "MAGAAS",
  DOI =          "http://dx.doi.org/10.2307/3621497",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue May 5 12:04:31 MDT 2015",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=MAG&volumeId=98&issueId=541;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathgazette2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  doi-bad =      "http://dx.doi.org/10.2307/3621497",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayBackIssues?jid=MAG",
}

@Article{Osler:2014:RFR,
  author =       "Thomas J. Osler and Tirupathi R. Chandrupatla",
  title =        "98.23 Recursive formulas related to the
                 {Arithmetic--Geometric Mean}",
  journal =      j-MATH-GAZ,
  volume =       "98",
  number =       "543",
  pages =        "484--486",
  month =        nov,
  year =         "2014",
  CODEN =        "MAGAAS",
  DOI =          "http://dx.doi.org/10.1017/S0025557200008202",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue Nov 17 09:58:03 MST 2015",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=MAG&volumeId=98&issueId=543;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayBackIssues?jid=MAG",
}

@Article{Villarino:2014:ASP,
  author =       "Mark B. Villarino",
  title =        "The {AGM} Simple Pendulum",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--19",
  day =          "1",
  month =        sep,
  year =         "2014",
  bibdate =      "Tue Mar 14 18:11:41 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "https://arxiv.org/pdf/1202.2782.pdf",
  abstract =     "We present a self-contained development of Gauss'
                 Arithmetic--Geometric Mean (AGM) and the work of the
                 great British number theorist A. E. Ingham who obtained
                 rigorous error bounds for the AGM's approximations to
                 the period of a simple pendulum. Moreover we discuss
                 the relation of complex multiplication to the AGM.",
  acknowledgement = ack-nhfb,
  remark =       "From page 2: ``It is unfortunate that none of the
                 authors [\cite{Carvalhaes:2008:APS} and Alfred George
                 Greenhill \booktitle{The Applications of Elliptic
                 Functions} (1892, 1959)] cites the marvelous
                 investigations of the great British number theorist A.
                 E. [Albert Edward] Ingham [(1900--1967)] which L. A.
                 Pars describes in his monumental 665-page standard work
                 \cite{Pars:1965:TAD,Pars:1968:TAD,Pars:1979:TAD}, which
                 was published almost 50 years ago in 1965. Ingham not
                 only obtains the formulas of Carvalhaes and Suppes
                 [\cite{Carvalhaes:2008:APS}] but also obtains rigorous
                 error estimates, both in excess and in defect. It is
                 beyond question that Ingham's work deserves to be
                 better known.'' [I cannot spot
                 elliptic-function-related work by Ingham in the 28
                 entries found in the MathSciNet database.]",
}

@Article{Yang:2014:SBA,
  author =       "Zhen-Hang Yang and Ying-Qing Song and Yu-Ming Chu",
  title =        "Sharp bounds for the arithmetic--geometric mean",
  journal =      j-J-INEQUAL-APPL,
  pages =        "2014:192",
  year =         "2014",
  DOI =          "http://dx.doi.org/10.1186/1029-242X-2014-192",
  ISSN =         "1029-242X",
  MRclass =      "26E60 (26D07 33E05)",
  MRnumber =     "3255894",
  MRreviewer =   "Huan Nan Shi",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Inequalities and Applications",
  journal-URL =  "http://journalofinequalitiesandapplications.springeropen.com/",
  pagecount =    "13",
}

@Article{Zuo:2014:UBS,
  author =       "Hongliang Zuo and Masatoshi Fujii and Jun Ichi Fujii
                 and Yuki Seo",
  title =        "Upper bound for spectra of {Jensen} operator and its
                 application to reverse arithmetic--geometric means",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "17",
  number =       "2",
  pages =        "641--648",
  year =         "2014",
  DOI =          "http://dx.doi.org/10.7153/mia-17-47",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "47A10 (47A30)",
  MRnumber =     "3235036",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Audenaert:2015:IBA,
  author =       "Koenraad M. R. Audenaert",
  title =        "Interpolating between the arithmetic--geometric mean
                 and {Cauchy--Schwarz} matrix norm inequalities",
  journal =      j-OPER-MATRICES,
  volume =       "9",
  number =       "2",
  pages =        "475--479",
  year =         "2015",
  DOI =          "http://dx.doi.org/10.7153/oam-09-29",
  ISSN =         "1846-3886 (print), 1848-9974 (electronic)",
  MRclass =      "15A60",
  MRnumber =     "3338577",
  MRreviewer =   "Rajendra Bhatia",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Operators and Matrices",
  journal-URL =  "http://oam.ele-math.com/",
}

@Article{Buric:2015:AEA,
  author =       "Tomislav Buri{\'c} and Neven Elezovi{\'c}",
  title =        "Asymptotic expansion of the arithmetic--geometric mean
                 and related inequalities",
  journal =      j-J-MATH-INEQUAL,
  volume =       "9",
  number =       "4",
  pages =        "1181--1190",
  year =         "2015",
  DOI =          "http://dx.doi.org/10.7153/jmi-09-90",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "26E60 (41A60)",
  MRnumber =     "3360162",
  MRreviewer =   "Silvia Toader",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Gao:2015:DWM,
  author =       "Peng Gao",
  title =        "On a discrete weighted mixed arithmetic--geometric
                 mean inequality",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "18",
  number =       "3",
  pages =        "941--947",
  year =         "2015",
  DOI =          "http://dx.doi.org/10.7153/mia-18-70",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "26E60 (26D15)",
  MRnumber =     "3344739",
  MRreviewer =   "Eder Kikianty",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Nishimura:2015:NPL,
  author =       "Ryo Nishimura",
  title =        "New properties of the lemniscate function and its
                 transformation",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "427",
  number =       "1",
  pages =        "460--468",
  year =         "2015",
  CODEN =        "JMANAK",
  DOI =          "http://dx.doi.org/10.1016/j.jmaa.2015.02.066",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X15001870",
  abstract =     "In this paper, we show several formulas for the
                 lemniscate function which include an infinite product
                 formula for the lemniscate sine. Furthermore, we show
                 the relation between the product formula and Carlson's
                 algorithm which is known as the variant of the
                 arithmetic geometric mean of Gauss.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Hypergeometric series; Infinite products; Lemniscate
                 function; Mean iteration",
}

@Article{Osler:2015:PNR,
  author =       "Thomas J. Osler",
  title =        "A Product of Nested Radicals for the {AGM}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "122",
  number =       "9",
  pages =        "886--887",
  month =        nov,
  year =         "2015",
  CODEN =        "AMMYAE",
  DOI =          "http://dx.doi.org/10.4169/amer.math.monthly.122.9.886",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Feb 8 16:33:32 MST 2016",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib",
  URL =          "http://www.jstor.org/stable/10.4169/amer.math.monthly.122.9.886",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{Ruan:2015:NAG,
  author =       "Jiechang Ruan",
  title =        "Notes on the arithmetic--geometric mean inequality for
                 singular values",
  journal =      j-ITAL-J-PURE-APPL-MATH,
  number =       "35",
  pages =        "227--232",
  year =         "2015",
  ISSN =         "1126-8042 (print), 2239-0227 (electronic)",
  MRclass =      "15A42 (47A63 47B15)",
  MRnumber =     "3477563",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Italian Journal of Pure and Applied Mathematics",
  journal-URL =  "http://ijpam.uniud.it/journal/",
}

@Article{Zou:2015:IAG,
  author =       "Limin Zou and Youyi Jiang",
  title =        "Improved arithmetic--geometric mean inequality and its
                 application",
  journal =      j-J-MATH-INEQUAL,
  volume =       "9",
  number =       "1",
  pages =        "107--111",
  year =         "2015",
  DOI =          "http://dx.doi.org/10.7153/jmi-09-10",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "47A63 (26D07 26E60)",
  MRnumber =     "3333909",
  MRreviewer =   "Ali Morassaei",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Zou:2015:RAG,
  author =       "Limin Zou and Yi Huang",
  title =        "A refinement of the arithmetic--geometric mean
                 inequality",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "46",
  number =       "1",
  pages =        "158--160",
  year =         "2015",
  CODEN =        "IJMEBM",
  DOI =          "http://dx.doi.org/10.1080/0020739X.2014.941426",
  ISSN =         "0020-739x (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  MRclass =      "26D15",
  MRnumber =     "3286728",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  journal-URL =  "http://www.tandfonline.com/loi/tmes20",
}

@Article{Zuo:2015:IRA,
  author =       "Hongliang Zuo and Nan Cheng",
  title =        "Improved reverse arithmetic--geometric means
                 inequalities for positive operators on {Hilbert}
                 space",
  journal =      j-MATH-INEQUAL-APPL,
  volume =       "18",
  number =       "1",
  pages =        "51--60",
  year =         "2015",
  DOI =          "http://dx.doi.org/10.7153/mia-18-03",
  ISSN =         "1331-4343 (print), 1848-9966 (electronic)",
  MRclass =      "47A30 (47A63)",
  MRnumber =     "3277056",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Inequalities \& Applications",
  journal-URL =  "http://mia.ele-math.com/",
}

@Article{Adiyasuren:2016:RAG,
  author =       "Vandanjav Adiyasuren and Tserendorj Batbold and
                 Muhammad Adil Khan",
  title =        "Refined arithmetic--geometric mean inequality and new
                 entropy upper bound",
  journal =      j-COMMUN-KOREAN-MATH-SOC,
  volume =       "31",
  number =       "1",
  pages =        "95--100",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.4134/CKMS.2016.31.1.095",
  ISSN =         "1225-1763 (print), 2234-3024 (electronic)",
  MRclass =      "94A17 (26E60)",
  MRnumber =     "3458733",
  MRreviewer =   "Flavia-Corina Mitroi-Symeonidis",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Korean Mathematical Society. Communications",
  journal-URL =  "http://ckms.kms.or.kr/",
}

@InCollection{Agarwal:2016:BGC,
  author =       "Ravi Agarwal and Hans Agarwal and Syamal Sen",
  title =        "Birth, growth and computation of pi to ten trillion
                 digits (2013)",
  crossref =     "Bailey:2016:PNG",
  pages =        "363--423",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_22",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Almkvist:2016:GLR,
  author =       "Gert Almkvist and Bruce Berndt",
  title =        "{Gauss}, {Landen}, {Ramanujan}, the
                 arithmetic--geometric mean, ellipses, $ \pi $, and the
                 {{\booktitle{Ladies Diary}}} (1988)",
  crossref =     "Bailey:2016:PNG",
  pages =        "125--150",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_8",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Bailey:2016:CDD,
  author =       "David H. Bailey",
  title =        "The computation of $ \pi $ to 29,360,000 decimal
                 digits using {Borweins}' quartically convergent
                 algorithm (1988)",
  crossref =     "Bailey:2016:PNG",
  pages =        "109--124",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_7",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Bailey:2016:CPI,
  author =       "David H. Bailey and Jonathan M. Borwein and Andrew
                 Mattingly and Glenn Wightwick",
  title =        "The computation of previously inaccessible digits of $
                 \pi $",
  crossref =     "Bailey:2016:PNG",
  pages =        "327--339",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_20",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Bailey:2016:RCV,
  author =       "David H. Bailey and Peter B. Borwein and Simon
                 Plouffe",
  title =        "On the rapid computation of various polylogarithmic
                 constants (1997)",
  crossref =     "Bailey:2016:PNG",
  pages =        "219--231",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_?",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bakherad:2016:RRG,
  author =       "Mojtaba Bakherad",
  title =        "Refinements of a reversed {AM--GM} operator
                 inequality",
  journal =      j-LIN-MULT-ALGEBRA,
  volume =       "64",
  number =       "9",
  pages =        "1687--1695",
  year =         "2016",
  CODEN =        "LNMLAZ",
  DOI =          "http://dx.doi.org/10.1080/03081087.2015.1114984",
  ISSN =         "0308-1087 (print), 1563-5139 (electronic)",
  ISSN-L =       "0308-1087",
  bibdate =      "Tue Sep 20 15:15:01 MDT 2016",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/linmultalgebra.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Multilinear Algebra",
  journal-URL =  "http://www.tandfonline.com/loi/glma20",
  onlinedate =   "01 Dec 2015",
}

@InCollection{Borwein:2016:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The arithmetic--geometric mean and fast computation of
                 elementary functions (1984)",
  crossref =     "Bailey:2016:PNG",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "79--96",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_4",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-319-32377-0_4",
  acknowledgement = ack-nhfb,
}

@InCollection{Borwein:2016:RME,
  author =       "Jonathan M. Borwein and Peter B. Borwein and David H.
                 Bailey",
  title =        "{Ramanujan}, modular equations, and approximations to
                 pi or how to compute one billion digits of pi (1989)",
  crossref =     "Bailey:2016:PNG",
  pages =        "175--195",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_?",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Brent:2016:FMP,
  author =       "Richard P. Brent",
  title =        "Fast multiple-precision evaluation of elementary
                 functions (1976)",
  crossref =     "Bailey:2016:PNG",
  pages =        "9--20",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_2",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Buric:2016:AAI,
  author =       "Tomislav Buri{\'c}",
  title =        "Asymptotic analysis of the iterative power means",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "433",
  number =       "1",
  pages =        "701--705",
  year =         "2016",
  CODEN =        "JMANAK",
  DOI =          "http://dx.doi.org/10.1016/j.jmaa.2015.08.020",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X15007477",
  abstract =     "We investigate the asymptotic expansion of the
                 compound mean obtained by the iterative process of two
                 power means. We present the stationary and convergence
                 properties of the coefficients in the expansions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Arithmetic--geometric mean; Asymptotic expansion;
                 Compound mean; Power mean",
}

@Article{Cardoso:2016:MAG,
  author =       "Jo{\~a}o R. Cardoso and Rui Ralha",
  title =        "Matrix Arithmetic--Geometric Mean and the Computation
                 of the Logarithm",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "37",
  number =       "2",
  pages =        "719--743",
  month =        "????",
  year =         "2016",
  CODEN =        "SJMAEL",
  DOI =          "http://dx.doi.org/10.1137/140998226",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F60 (33E05 65F30)",
  MRnumber =     "3507553",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/2;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2016",
}

@InCollection{Cox:2016:AGM,
  author =       "David A. Cox",
  title =        "The arithmetic--geometric mean of {Gauss} (1984)",
  crossref =     "Bailey:2016:PNG",
  pages =        "21--78",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_3",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Article{Fujii:2016:RDM,
  author =       "Jun Ichi Fujii and Masatoshi Fujii and Yuki Seo and
                 Hongliang Zuo",
  title =        "Recent developments of matrix versions of the
                 arithmetic--geometric mean inequality",
  journal =      j-ANN-FUNCT-ANAL,
  volume =       "7",
  number =       "1",
  pages =        "102--117",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1215/20088752-3429400",
  ISSN =         "2008-8752",
  MRclass =      "47A63 (15A18 15A42 47-02 47A30)",
  MRnumber =     "3449343",
  MRreviewer =   "Rajendra Bhatia",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Functional Analysis",
  journal-URL =  "http://projecteuclid.org/afa",
}

@Article{Hirzallah:2016:SVC,
  author =       "Omar Hirzallah",
  title =        "Singular values of convex functions of operators and
                 the arithmetic--geometric mean inequality",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "433",
  number =       "2",
  pages =        "935--947",
  year =         "2016",
  CODEN =        "JMANAK",
  DOI =          "http://dx.doi.org/10.1016/j.jmaa.2015.08.036",
  ISSN =         "0022-247x (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "47A63",
  MRnumber =     "3398744",
  MRreviewer =   "Eizaburo Kamei",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022247X15007635",
  abstract =     "We prove singular value inequalities for convex
                 functions of products and sums of operators that
                 generalize the arithmetic--geometric mean inequality
                 for operators. Among other results, we prove that if $
                 A_i, B_i, X_i, Y_i $, $ i = 1, \ldots, n $ are
                 operators on a complex separable Hilbert space such
                 that $ | X_i | 2 + | Y_i | 2 2 n \leq I $, $ i = 1,
                 \ldots, n $ and if $f$ is a nonnegative increasing
                 convex function on $ [0, \infty)$ satisfying $ f (0) =
                 0$, then $ s_j (f (| \sum_{i = 1}^n A_i X_i Y_i^\star
                 B_i^\star |)) \leq (1 / 2) s_j (\oplus_{k = 1}^n
                 (X_k^\star (\sum_{i = 1}^n f(| A_i^\star A_k |)) X_k +
                 Y_k^\star (\sum_{i = 1}^n f(| B_i^\star B_k |)) Y_k))$
                 for $ j = 1, 2, \ldots $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
  keywords =     "Compact operator; Convex function; Inequality;
                 Positive operator; Singular value",
}

@Article{Israel:2016:AGM,
  author =       "Arie Israel and Felix Krahmer and Rachel Ward",
  title =        "An arithmetic--geometric mean inequality for products
                 of three matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "488",
  number =       "??",
  pages =        "1--12",
  day =          "1",
  month =        jan,
  year =         "2016",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2015.09.013",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "15A45",
  MRnumber =     "3419770",
  MRreviewer =   "Tanvi Jain",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/linala2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379515005285",
  abstract =     "Consider the following noncommutative
                 arithmetic--geometric mean inequality: Given
                 positive-semidefinite matrices $ A_1, \ldots, A_n $,
                 the following holds for each integer $ m \leq n $: $ (1
                 / n^m) \sum_{j_1, j_2, \ldots, j_m = 1}^n ||| A_{j_1}
                 A_{j_2} \ldots A_{j_m} ||| \geq ((n - m)! / n!)
                 \sum_{j_1, j_2, \ldots, j_m} = 1 ({\rm all distinct})^n
                 ||| A_{j_1} A_{j_2} \ldots A_{j_m} ||| $, where $ |||
                 \cdot ||| $ denotes a unitarily invariant norm,
                 including the operator norm and Schatten $p$-norms as
                 special cases. While this inequality in full generality
                 remains a conjecture, we prove that the inequality
                 holds for products of up to three matrices, $ m \leq
                 3$. The proofs for $ m = 1, 2$ are straightforward; to
                 derive the proof for $ m = 3$, we appeal to a variant
                 of the classic Araki--Lieb--Thirring inequality for
                 permutations of matrix products.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
  keywords =     "Arithmetic--geometric mean inequality; Linear algebra;
                 Norm inequalities",
}

@InCollection{Kanada:2016:VMP,
  author =       "Yasumasa Kanada",
  title =        "Vectorization of multiple-precision arithmetic program
                 and 201,326,000 decimal digits of pi calculation
                 (1988)",
  crossref =     "Bailey:2016:PNG",
  pages =        "151--164",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_9",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Newman:2016:SVF,
  author =       "D. J. Newman",
  title =        "A simplified version of the fast algorithms of {Brent}
                 and {Salamin} (1985)",
  crossref =     "Bailey:2016:PNG",
  pages =        "97--102",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_5",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Salamin:2016:CUA,
  author =       "Eugene Salamin",
  title =        "Computation of $ \pi $ using arithmetic--geometric
                 mean (1976)",
  crossref =     "Bailey:2016:PNG",
  pages =        "1--8",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0_1",
  bibdate =      "Tue Mar 14 11:34:57 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Singh:2016:PAL,
  author =       "Paramanand Singh",
  title =        "$ \pi $ ({PI}) and the {AGM}: {Legendre}'s Identity",
  howpublished = "Web site",
  year =         "2016",
  bibdate =      "Tue Mar 14 10:19:25 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "https://paramanands.blogspot.com/2009/08/pi-and-the-agm-legendres-identity.html",
  acknowledgement = ack-nhfb,
}

@Article{Wang:2016:OBG,
  author =       "Hua Wang and Wei-Mao Qian and Yu-Ming Chu",
  title =        "Optimal bounds for {Gaussian} arithmetic--geometric
                 mean with applications to complete elliptic integral",
  journal =      j-FUNCT-SPACES,
  pages =        "Art. ID 3698463, 6",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1155/2016/3698463",
  ISSN =         "2314-8896",
  MRclass =      "26E60 (33E05)",
  MRnumber =     "3531324",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Function Spaces",
  journal-URL =  "https://www.hindawi.com/journals/jfs/",
}

@Article{Zou:2016:AGM,
  author =       "Limin Zou",
  title =        "An arithmetic--geometric mean inequality for singular
                 values and its applications",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "",
  number =       "??",
  pages =        "-",
  year =         "2016",
  CODEN =        "LAAPAW",
  DOI =          "http://dx.doi.org/10.1016/j.laa.2016.01.016",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379516000185",
  abstract =     "In this short note, we give a new equivalent form of
                 the arithmetic--geometric mean inequality for singular
                 values. As applications of our result, we give a new
                 proof of an inequality due to Bhatia and Davis (1993)
                 [4] and we obtain a singular value inequality for
                 matrix means, which is similar to one proved by Drury
                 (2012) [9]. Finally, we present a log-majorization
                 inequality for singular values.",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
  keywords =     "Matrix means; Singular values; Unitarily invariant
                 norms",
}

@Article{Zou:2016:NIB,
  author =       "Limin Zou and Youyi Jiang",
  title =        "A note on interpolation between the
                 arithmetic--geometric mean and {Cauchy--Schwarz} matrix
                 norm inequalities",
  journal =      j-J-MATH-INEQUAL,
  volume =       "10",
  number =       "4",
  pages =        "1119--1122",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.7153/jmi-10-88",
  ISSN =         "1846-579x (print), 1848-9575 (electronic)",
  MRclass =      "15A60 (47A63)",
  MRnumber =     "3581159",
  bibdate =      "Tue Mar 14 07:52:56 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Inequalities",
  journal-URL =  "http://jmi.ele-math.com/",
}

@Article{Buric:2017:CAA,
  author =       "Tomislav Buri{\'c} and Neven Elezovi{\'c}",
  title =        "Computation and analysis of the asymptotic expansions
                 of the compound means",
  journal =      j-APPL-MATH-COMP,
  volume =       "303",
  number =       "??",
  pages =        "48--54",
  year =         "2017",
  CODEN =        "AMHCBQ",
  DOI =          "http://dx.doi.org/10.1016/j.amc.2017.01.025",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Mar 14 16:13:28 2017",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300317300334",
  abstract =     "We derive algorithms for computing asymptotic
                 expansion of the composite mean of two arbitrary means
                 M and N. Then we analyse asymptotic behaviour of the
                 compound mean $ M \otimes N $. Examples and application
                 to some classical means are also presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "Arithmetic--geometric mean; Asymptotic expansion;
                 Compound mean; Power mean",
}

%%% ====================================================================
%%% Cross-referenced entries must come last:
@Proceedings{Traub:1976:ACC,
  editor =       "J. F. (Joseph Frederick) Traub",
  booktitle =    "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  title =        "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "ix + 239",
  year =         "1976",
  ISBN =         "0-12-697560-4",
  ISBN-13 =      "978-0-12-697560-4",
  LCCN =         "QA297 .S915 1975",
  bibdate =      "Sun Dec 30 18:48:22 MST 2007",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  meetingname =  "Symposium on Analytic Computational Complexity,
                 Carnegie-Mellon University, 1975.",
  remark =       "",
  subject =      "Numerical analysis; Data processing; Congresses;
                 Computational complexity",
}

@Proceedings{Martin:1988:SPN,
  editor =       "Joanne L. Martin and Stephen F. Lundstrom",
  booktitle =    "Supercomputing '88: proceedings, November 14--18,
                 1988, Orlando, Florida",
  title =        "Supercomputing '88: proceedings, November 14--18,
                 1988, Orlando, Florida",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "viii + 263",
  year =         "1988",
  ISBN =         "0-8186-0882-X (v. 1; paper), 0-8186-8882-3 (v. 1;
                 case), 0-8186-4882-1 (v. 1: microfiche) 0-8186-8923-4
                 (v. 2), 0-8186-5923-X (v. 2: microfiche), 0-8186-8923-4
                 (v. 2: case)",
  ISBN-13 =      "978-0-8186-0882-7 (v. 1; paper), 978-0-8186-8882-9 (v.
                 1; case), 978-0-8186-4882-3 (v. 1: microfiche)
                 978-0-8186-8923-9 (v. 2), 978-0-8186-5923-2 (v. 2:
                 microfiche), 978-0-8186-8923-9 (v. 2: case)",
  LCCN =         "QA76.5 .S894 1988",
  bibdate =      "Fri Aug 30 08:01:51 MDT 1996",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib",
  note =         "Two volumes. IEEE catalog number 88CH2617-9. IEEE
                 Computer Society Order Number 882.",
  acknowledgement = ack-nhfb,
  classification = "C5440 (Multiprocessor systems and techniques); C7300
                 (Natural sciences)",
  keywords =     "biology computing; chemistry; computational biology;
                 computational fluid dynamics; computational
                 mathematics; computational physics; flow simulation;
                 global change; mathematics computing; parallel
                 processing; physics computing; structural analysis;
                 structural engineering computing; supercomputers ---
                 congresses",
}

@Proceedings{Adams:1993:SCA,
  editor =       "E. Adams and U. Kulisch",
  booktitle =    "Scientific computing with automatic result
                 verification",
  title =        "Scientific computing with automatic result
                 verification",
  volume =       "189",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "x + 612",
  year =         "1993",
  ISBN =         "0-12-044210-8",
  ISBN-13 =      "978-0-12-044210-2",
  LCCN =         "QA76.S368 1993",
  bibdate =      "Mon Dec 18 10:27:38 1995",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib",
  series =       "Mathematics in science and engineering",
  acknowledgement = ack-nhfb,
}

@Proceedings{Cohen:1995:AAA,
  editor =       "G. (G{\'e}rard) Cohen and Marc Giusti and Teo Mora",
  booktitle =    "{Applied algebra, algebraic algorithms, and
                 error-correcting codes: 11th international symposium,
                 AAECC-11, Paris, France, July 1995: proceedings}",
  title =        "{Applied algebra, algebraic algorithms, and
                 error-correcting codes: 11th international symposium,
                 AAECC-11, Paris, France, July 1995: proceedings}",
  volume =       "948",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 484",
  year =         "1995",
  ISBN =         "3-540-60114-7 (softcover)",
  ISBN-13 =      "978-3-540-60114-2 (softcover)",
  LCCN =         "QA268 .A35 1995",
  bibdate =      "Tue Mar 14 15:37:05 MDT 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Lecture notes in computer science",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0815/95021560-d.html",
  acknowledgement = ack-nhfb,
  meetingname =  "AAECC-11 (1995: Paris, France)",
  subject =      "Error-correcting codes (Information theory);
                 Congresses; Algebra; Data processing; Algorithms",
}

@Proceedings{Alefeld:1996:SCV,
  editor =       "G{\"o}tz Alefeld and Andreas Frommer and Bruno Lang",
  booktitle =    "Scientific computing and validated numerics:
                 proceedings of the International Symposium on
                 Scientific Computing, Computer Arithmetic and Validated
                 Numerics SCAN-95 held in Wuppertal, Germany, September
                 26--29, 1995",
  title =        "Scientific computing and validated numerics:
                 proceedings of the International Symposium on
                 Scientific Computing, Computer Arithmetic and Validated
                 Numerics {SCAN}-95 held in Wuppertal, Germany,
                 September 26--29, 1995",
  volume =       "90",
  publisher =    "Akademie Verlag",
  address =      "Berlin, Germany",
  pages =        "340",
  year =         "1996",
  ISBN =         "3-05-501737-4",
  ISBN-13 =      "978-3-05-501737-7",
  ISSN =         "0138-3019",
  LCCN =         "QA76.95 .I575 1995",
  bibdate =      "Fri Mar 27 09:56:17 MST 1998",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Mathematical Research",
  acknowledgement = ack-nhfb,
}

@Proceedings{Broy:1996:DPD,
  editor =       "M. Broy",
  booktitle =    "{Deductive program design: Proceedings of the NATO
                 Advanced Study Institute on Deductive Program Design,
                 held in Marktoberdorf, Germany, July 26--August 7,
                 1994}",
  title =        "{Deductive program design: Proceedings of the NATO
                 Advanced Study Institute on Deductive Program Design,
                 held in Marktoberdorf, Germany, July 26--August 7,
                 1994}",
  volume =       "152",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 467",
  year =         "1996",
  ISBN =         "3-540-60947-4 (hardcover)",
  ISBN-13 =      "978-3-540-60947-6 (hardcover)",
  LCCN =         "QA76.9.D5 D38 1996",
  bibdate =      "Tue Mar 17 10:33:47 MDT 2015",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "NATO ASI series. Series F, Computer and systems
                 sciences",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0812/96010788-d.html",
  acknowledgement = ack-nhfb,
  subject =      "Electronic data processing; Distributed processing;
                 Congresses; System design; Logic, Symbolic and
                 mathematical",
}

@Book{Zhang:1996:AMI,
  editor =       "H. (Hantao) Zhang",
  booktitle =    "Automated Mathematical Induction",
  title =        "Automated Mathematical Induction",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "224",
  year =         "1996",
  DOI =          "http://dx.doi.org/10.1007/978-94-009-1675-3",
  ISBN =         "94-010-7250-7 (print), 94-009-1675-2 (e-book),",
  ISBN-13 =      "978-94-010-7250-2 (print), 978-94-009-1675-3
                 (e-book),",
  LCCN =         "Q334-342",
  bibdate =      "Tue Mar 14 12:17:31 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://public.eblib.com/choice/publicfullrecord.aspx?p=3102529",
  abstract =     "Two decades ago, Boyer and Moore built one of the
                 first automated theorem provers that was capable of
                 proofs by mathematical induction. Today, the
                 Boyer--Moore theorem prover remains the most successful
                 in the field. For a long time, the research on
                 automated mathematical induction was confined to very
                 few people. In recent years, as more people realize the
                 importance of automated inductive reasoning to the use
                 of formal methods of software and hardware development,
                 more automated inductive proof systems have been
                 built.\par

                 Three years ago, the interested researchers in the
                 field formed two consortia on automated inductive
                 reasoning --- the MInd consortium in Europe and the
                 IndUS consortium in the United States. The two
                 consortia organized three joint workshops in
                 1992--1995. There will be another one in 1996.
                 Following the suggestions of Alan Bundy and Deepak
                 Kapur, this book documents advances in the
                 understanding of the field and in the power of the
                 theorem provers that can be built.\par

                 In the first of six papers, the reader is provided with
                 a tutorial study of the Boyer--Moore theorem prover.
                 The other five papers present novel ideas that could be
                 used to build theorem provers more powerful than the
                 Boyer-Moore prover.",
  acknowledgement = ack-nhfb,
  subject =      "Computer science; Logic; Artificial intelligence;
                 Logic, Symbolic and mathematical; Artificial
                 intelligence; Computer science; Logic; Logic, Symbolic
                 and mathematical",
  tableofcontents = "Induction Using Term Orders \\
                 New Uses of Linear Arithmetic in Automated Theorem
                 Proving by Induction \\
                 Productive Use of Failure in Inductive Proof \\
                 Middle-Out Reasoning for Synthesis and Induction \\
                 A Calculus for and Termination of Rippling \\
                 Interaction with the Boyer Moore Theorem Prover: A
                 Tutorial Study Using the Arithmetic--Geometric Mean
                 Theorem",
}

@Book{Berggren:1997:PS,
  editor =       "Lennart Berggren and Jonathan Borwein and Peter
                 Borwein",
  booktitle =    "{Pi}, a sourcebook",
  title =        "{Pi}, a sourcebook",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xix + 716",
  year =         "1997",
  ISBN =         "0-387-94924-0",
  ISBN-13 =      "978-0-387-94924-6",
  LCCN =         "QA484 .P5 1997",
  bibdate =      "Sat Apr 23 09:55:09 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  subject =      "Pi",
}

@Book{Berggren:2000:PS,
  editor =       "Lennart Berggren and Jonathan Borwein and Peter
                 Borwein",
  booktitle =    "{Pi}, a sourcebook",
  title =        "{Pi}, a sourcebook",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xix + 736",
  year =         "2000",
  ISBN =         "0-387-98946-3 (hardcover)",
  ISBN-13 =      "978-0-387-98946-4 (hardcover)",
  LCCN =         "QA484 .P5 2000",
  bibdate =      "Mon Aug 10 17:48:29 MDT 2009",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
  subject =      "Pi (mathematical constant)",
}

@Book{Berggren:2004:PSB,
  editor =       "Lennart Berggren and Jonathan Borwein and Peter
                 Borwein",
  booktitle =    "{Pi}, a source book",
  title =        "{Pi}, a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "xix + 797",
  year =         "2004",
  ISBN =         "0-387-20571-3",
  ISBN-13 =      "978-0-387-20571-7",
  LCCN =         "QA484 .P5 2004",
  bibdate =      "Sat Apr 23 09:59:19 MDT 2011",
  bibsource =    "http://www.math.utah.edu/pub/tex/bib/agm.bib;
                 http://www.math.utah.edu/pub/tex/bib/pi.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0818/2003066023-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0818/2003066023-t.html",
  acknowledgement = ack-nhfb,
  remark =       "Fourth edition expected in 2011.",
  subject =      "Pi",
}

@Book{Arndt:2011:MC,
  author =       "J{\"o}rg Arndt",
  booktitle =    "Matters Computational",
  title =        "Matters Computational",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 966",
  year =         "2011",
  DOI =          "http://dx.doi.org/10.1007/978-3-642-14764-7",
  ISBN =         "3-642-14764-X, 3-642-14763-1",
  ISBN-13 =      "978-3-642-14764-7, 978-3-642-14763-0",
  LCCN =         "QA9.58 .A76 2011",
  bibdate =      "Tue Mar 14 15:06:32 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  abstract =     "This book provides algorithms and ideas for
                 computationalists. Subjects treated include low-level
                 algorithms, bit wizardry, combinatorial generation,
                 fast transforms like the Fourier transform, and fast
                 arithmetic for both real numbers and finite fields.
                 Various optimization techniques are described and the
                 actual performance of many given implementations is
                 examined. The focus is on material that does not
                 usually appear in textbooks on algorithms. The
                 implementations are done in C++ and the GP language,
                 written for POSIX-compliant platforms such as the Linux
                 and BSD operating systems.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Matters Computational \\
                 Preface \\
                 Contents \\
                 Part I: Low level algorithms \\
                 Part II:Combinatorial generation \\
                 Part III:Fast transforms \\
                 Part IV: Fast arithmetic \\
                 Part V: Algorithms for finite fields \\
                 Appendix A: The electronic version of the book \\
                 Appendix B: Machine used for benchmarking \\
                 Appendix C: The GP language \\
                 Bibliography \\
                 Index",
  subject =      "Mathematics",
  tableofcontents = "Low level algorithms \\
                 Bit wizardry / 2--101 \\
                 Permutations and their operations / 102--133 \\
                 Sorting and searching / 134--152 \\
                 Data structures / 153--170 \\
                 Combinatorial generation \\
                 Conventions and considerations / 172--175 \\
                 Combinations / 176--193 \\
                 Compositions / 194--201 \\
                 Subsets / 202--216 \\
                 Mixed radix numbers / 217--231 \\
                 Permutations / 232--276 \\
                 Permutations with special properties / 277--290 \\
                 $k$-permutations / 291--294 \\
                 Multisets / 295--303 \\
                 Gray codes for string with restrictions / 304--322 \\
                 Parenthesis strings / 323--338 \\
                 Integer partitions / 339--353 \\
                 Set partitions / 354--369 \\
                 Necklaces and Lyndon words / 370--383 \\
                 Hadamard and conference matrices / 384--390 \\
                 Searching paths in directed graphs / 391--408 \\
                 Fast transforms \\
                 The Fourier transform / 410--439 \\
                 Convolution, correlation, and more FFT algorithms /
                 440--458 \\
                 The Walsh transform and its relatives / 459--496 \\
                 The Haar transform / 497--514 \\
                 The Hartley transform / 515--534 \\
                 Number theoretic transforms (NTTs) / 535--542 \\
                 Fast wavelet transforms / 543--548 \\
                 Fast arithmetic \\
                 Fast multiplication and exponentiation / 550--566 \\
                 Root extraction / 567--586 \\
                 Iterations for the inversion of a function / 587--598
                 \\
                 The AGM, elliptic integrals, and algorithms for
                 computing / 599--621 \\
                 Logarithm and exponential function / 622--640 \\
                 Computing the elementary functions with limited
                 resources / 641--650 \\
                 Numerical evaluation of power series / 651--665 \\
                 Recurrences and Chebyshev polynomials / 666--684 \\
                 Hypergeometric series / 685--703 \\
                 Cyclotomic polynomials, product forms, and continued
                 fractions / 704--725 \\
                 Synthetic Iterations / 726--762 \\
                 Algorithms for finite fields \\
                 Modular arithmetic and some number theory / 764--821
                 \\
                 Binary polynomials / 822--863 \\
                 Shift registers / 864--885 \\
                 Binary finite fields: $ {\rm GF}(2^n) $ / 886--920 \\
                 The electronic version of the book \\
                 Machine used for benchmarking \\
                 The GP language \\
                 Bibliography \\
                 Index",
}

@Book{Bailey:2016:PNG,
  editor =       "David H. Bailey and Jonathan M. Borwein",
  booktitle =    "Pi: the next generation: a sourcebook on the recent
                 history of Pi and its computation",
  title =        "Pi: the next generation: a sourcebook on the recent
                 history of Pi and its computation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 507",
  year =         "2016",
  DOI =          "http://dx.doi.org/10.1007/978-3-319-32377-0",
  ISBN =         "3-319-32375-X, 3-319-32377-6 (e-book)",
  ISBN-13 =      "978-3-319-32375-6, 978-3-319-32377-0 (e-book)",
  LCCN =         "QA251",
  MRclass =      "01A75, 11-00, 65-00, 11-06, 65-06",
  bibdate =      "Fri Sep 30 09:43:05 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 http://www.math.utah.edu/pub/tex/bib/agm.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/1716/;
                 http://lib.myilibrary.com?id=941862",
  ZMnumber =     "1342.01042",
  acknowledgement = ack-nhfb,
  subject =      "Pi",
  tableofcontents = "Computation of $\pi$ using arithmetic--geometric
                 mean (1976) / Salamin, Eugene / 1--8 \\
                 Fast multiple-precision evaluation of elementary
                 functions (1976) / Brent, Richard P. / 9--20 \\
                 The arithmetic--geometric mean of Gauss (1984) / Cox,
                 David A. / 21--78 \\
                 The arithmetic--geometric mean and fast computation of
                 elementary functions (1984) / Borwein, J. M. and
                 Borwein, P. B. / 79--96 \\
                 A simplified version of the fast algorithms of Brent
                 and Salamin (1985) / Newman, D. J. / 97--102 \\
                 Is pi normal? (1985) / Wagon, S. / 103--107 \\
                 The computation of $\pi$ to 29,360,000 decimal digits
                 using Borweins' quartically convergent algorithm (1988)
                 / Bailey, David H. / 109--124 \\
                 Gauss, Landen, Ramanujan, the arithmetic--geometric
                 mean, ellipses, $\pi$, and the Ladies Diary (1988) /
                 Almkvist, Gert (et al.) / 125--150 \\
                 Vectorization of multiple-precision arithmetic program
                 and 201,326,000 decimal digits of pi calculation (1988)
                 / Kanada, Yasumasa / 151--164 \\
                 Ramanujan and pi (1988) / Borwein, Jonathan M. (et al.)
                 / 165--174 \\
                 Ramanujan, modular equations, and approximations to pi
                 or how to compute one billion digits of pi (1989) /
                 Borwein, Jonathan M. (et al.) / 175--195 \\
                 Pi, Euler numbers, and asymptotic expansions (1989) /
                 Borwein, Jonathan M. (et al.) / 197--205 \\
                 A spigot algorithm for the digits of $\pi$ (1995) /
                 Rabinowitz, Stanley (et al.) / 207--217 \\
                 On the rapid computation of various polylogarithmic
                 constants (1997) / Bailey, David H. (et al.) / 219--231
                 \\
                 Similarities in irrationality proofs for $\pi$, ln 2,
                 \zeta(2), and \zeta(3) (2001) / Huylebrouck, Dirk /
                 233--244 \\
                 Unbounded spigot algorithms for the digits of pi (2006)
                 / Gibbons, Jeremy / 245--257 \\
                 Mathematics by experiment: Plausible reasoning in the
                 21st Century (2008) / Bailey, David H. (et al.) /
                 259--291 \\
                 Approximations to $\pi$ derived from integrals with
                 nonnegative integrands (2009) / Lucas, Stephen K. /
                 293--301 \\
                 Ramanujan's series for 1/$\pi$: A survey (2009) /
                 Baruah, Nayandeep Deka (et al.) / 303--325 \\
                 The computation of previously inaccessible digits of
                 $\pi$ / Bailey, David H. (et al.) / 327--339 \\
                 Walking on real numbers (2013) / Artacho, Francisco J.
                 Arag{\'o}n (et al.) / 341--361 \\
                 Birth, growth and computation of pi to ten trillion
                 digits (2013) / Agarwal, Ravi (et al.) / 363--423 \\
                 Pi day is upon us again and we still do not know if pi
                 is normal (2014) / Bailey, David H. (et al.) / 425--442
                 \\
                 The Life of $\pi$ (2014) / Borwein, Jonathan M. (et
                 al.) / 443--474 \\
                 I prefer pi: A brief history and anthology of articles
                 in the American Mathematical Monthly (2015) / Borwein,
                 Jonathan M. / 475--499",
}