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155 S 1400 E RM 233,
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FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
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@MastersThesis{Hestenes:1928:PRS,
author = "Magnus Rudolph Hestenes",
title = "Path of a Rotating Sphere",
type = "{M.A.} thesis",
school = "University of Wisconsin-Madison",
address = "Madison, WI, USA",
pages = "160",
year = "1928",
bibdate = "Tue Oct 24 11:11:23 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://books.google.com/books?id=P242AAAAMAAJ",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InCollection{Hestenes:1931:SCG,
author = "M. R. Hestenes",
title = "Sufficient conditions for the general problem of
{Mayer} with variable end-points",
crossref = "Hestenes:1933:CCV",
pages = "339--359",
year = "1931",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
jfm = "59.1147.06",
ZBmath = "2546605",
}
@Article{Bliss:1932:SCP,
author = "G. A. Bliss and M. R. Hestenes",
title = "Sufficient conditions for a problem of {Mayer} in the
calculus of variations",
journal = j-BULL-AMS,
volume = "38",
number = "5",
pages = "347--348",
month = may,
year = "1932",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1933-05727-0",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1932-38-05/S0002-9904-1932-05405-2/S0002-9904-1932-05405-2.pdf",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
jfm = "58.0541.05",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
received = "8 April 1932",
ZBmath = "2550653",
}
@PhdThesis{Hestenes:1932:SCG,
author = "Magnus Rudolf Hestenes",
title = "Sufficient Conditions for the General Problem of
{Mayer} with Variable End-Points",
type = "{Ph.D.} dissertation",
school = "Department of Mathematics, University of Chicago",
address = "Chicago, IL, USA",
pages = "iii + 19",
month = jun,
year = "1932",
bibdate = "Tue Oct 24 10:52:54 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "http://pi.lib.uchicago.edu/1001/cat/bib/4527495;
https://www.proquest.com/pqdtglobal/docview/301826467/",
acknowledgement = ack-nhfb,
advisor = "Gilbert Ames Bliss",
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Hestenes:1932:SCP,
author = "M. R. Hestenes",
title = "Sufficient conditions for a problem of {Mayer} with
variable endpoints",
journal = j-BULL-AMS,
volume = "38",
number = "5",
pages = "348--348",
month = may,
year = "1932",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1933-05727-0",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1932-38-05/S0002-9904-1932-05405-2/S0002-9904-1932-05405-2.pdf",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
jfm = "58.0541.04",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
received = "8 April 1932",
ZBmath = "2550652",
}
@Article{Bliss:1933:NPB,
author = "G. A. Bliss and M. R. Hestenes",
title = "A note on the problem of {Bolza} in the calculus of
variations",
journal = j-BULL-AMS,
volume = "39",
number = "5",
pages = "341--341",
month = may,
year = "1933",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1933-05727-0",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1933-39-05/S0002-9904-1933-05620-3/S0002-9904-1933-05620-3.pdf",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
jfm = "59.0505.07",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
received = "22 March 1933",
ZBmath = "2544076",
}
@InCollection{Bliss:1933:SCP,
author = "G. A. Bliss and M. R. Hestenes",
title = "Sufficient conditions for a problem of {Mayer} in the
calculus of variations",
crossref = "Hestenes:1933:CCV",
pages = "295--337",
year = "1933",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
jfm = "59.1148.01",
ZBmath = "2546606",
}
@Article{Hestenes:1933:NJC,
author = "M. R. Hestenes",
title = "A note on the {Jacobi} condition for parametric
problems in the calculus of variations",
journal = j-BULL-AMS,
volume = "39",
number = "7",
pages = "509--509",
month = jul,
year = "1933",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1933-39-07/S0002-9904-1933-05674-4/S0002-9904-1933-05674-4.pdf",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
jfm = "59.0506.01",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
received = "23 May 1933",
ZBmath = "2544079",
}
@Article{Hestenes:1933:SCG,
author = "M. R. Hestenes",
title = "Sufficient conditions for the general problem of
{Mayer} with variable end points",
journal = j-TRANS-AM-MATH-SOC,
volume = "35",
number = "2",
pages = "479--490",
month = apr,
year = "1933",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1989777",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0006.35001",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ZBmath = "2544052, 3008879",
}
@Article{Hestenes:1933:SCPa,
author = "M. R. Hestenes and G. A. Bliss",
title = "Sufficient Conditions for a Problem of {Mayer} in the
Calculus of Variations",
journal = j-TRANS-AM-MATH-SOC,
volume = "35",
number = "1",
pages = "305--326",
month = jan,
year = "1933",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1989326",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
bibdate = "Tue Oct 24 13:00:48 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0006.25903",
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
remark = "TO DO: Check author order",
ZBmath = "2544051, 3008512",
}
@Article{Hestenes:1933:SCPb,
author = "M. R. Hestenes",
title = "Sufficient conditions for the problem of {Lagrange} in
the calculus of variations",
journal = j-BULL-AMS,
volume = "39",
number = "5",
pages = "341--341",
month = may,
year = "1933",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1933-05620-3",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1933-39-05/S0002-9904-1933-05620-3/S0002-9904-1933-05620-3.pdf",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
jfm = "59.0505.08",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
received = "8 April 1933",
ZBmath = "2544077",
}
@Article{Hestenes:1933:SCPc,
author = "M. R. Hestenes",
title = "Sufficient conditions for the problem of {Bolza} in
the calculus of variations",
journal = j-BULL-AMS,
volume = "39",
number = "7",
pages = "506--506",
month = jul,
year = "1933",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1933-39-07/S0002-9904-1933-05674-4/S0002-9904-1933-05674-4.pdf",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
jfm = "59.0505.09",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
received = "23 May 1933",
ZBmath = "2544078",
}
@Article{Hestenes:1934:BTP,
author = "M. R. Hestenes",
title = "A basis theorem in the problems of {Lagrange} and
{Bolza}",
journal = j-BULL-AMS,
volume = "40",
number = "11",
pages = "802--803",
month = nov,
year = "1934",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1934-05855-5",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1934-40-11/S0002-9904-1934-05986-X/S0002-9904-1934-05986-X.pdf",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
jfm = "60.0461.04",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
received = "24 October 1934",
ZBmath = "2538275",
}
@Article{Hestenes:1934:NJC,
author = "M. R. Hestenes",
title = "A note on the {Jacobi} condition for parametric
problems in the calculus of variations",
journal = j-BULL-AMS,
volume = "40",
number = "4",
pages = "297--302",
month = apr,
year = "1934",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1934-05855-5",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1934-40-04/S0002-9904-1934-05855-5/;
https://www.ams.org/journals/bull/1934-40-04/S0002-9904-1934-05855-5/S0002-9904-1934-05855-5.pdf",
ZMnumber = "0010.02703",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
remark = "Presented 23 June 1933.",
ZBmath = "2538259, 3014483",
}
@Article{Hestenes:1934:PBC,
author = "M. R. Hestenes",
title = "The problem of {Bolza} in the calculus of variations
in parametric form",
journal = j-BULL-AMS,
volume = "40",
number = "9",
pages = "657--657",
month = sep,
year = "1934",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1934-05855-5",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1934-40-09/S0002-9904-1934-05918-4/S0002-9904-1934-05918-4.pdf",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
jfm = "60.0461.03",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
received = "28 July 1934",
ZBmath = "2538274",
}
@Article{Hestenes:1934:SCPa,
author = "M. R. Hestenes",
title = "Sufficient Conditions for the Problem of {Bolza} in
the Calculus of Variations",
journal = j-TRANS-AM-MATH-SOC,
volume = "36",
number = "4",
pages = "793--818",
month = oct,
year = "1934",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1989824",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
bibdate = "Tue Oct 24 13:00:48 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0010.30602",
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ZBmath = "2538260, 3015622",
}
@Article{Hestenes:1934:SCPb,
author = "M. R. Hestenes",
title = "Sufficient conditions for the problem of {Bolza} in
the calculus of variations. {II}",
journal = j-BULL-AMS,
volume = "40",
number = "3",
pages = "220--220",
month = mar,
year = "1934",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1934-05855-5",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1934-40-03/S0002-9904-1934-05818-X/S0002-9904-1934-05818-X.pdf",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
jfm = "60.0461.02",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
received = "23 February 1934",
ZBmath = "2538273",
}
@Article{Birkhoff:1935:GMPa,
author = "G. D. Birkhoff and M. R. Hestenes",
title = "Generalized Minimax Principle in the Calculus of
Variations",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "21",
number = "2",
pages = "96--99",
month = feb,
year = "1935",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.21.2.96",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Wed Oct 25 10:45:03 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/content/by/year",
}
@Article{Birkhoff:1935:GMPb,
author = "G. D. Birkhoff and M. R. Hestenes",
title = "Generalized minimax principle in the calculus of
variations",
journal = j-DUKE-MATH-J,
volume = "1",
number = "4",
pages = "413--432",
month = dec,
year = "1935",
CODEN = "DUMJAO",
DOI = "https://doi.org/10.1215/S0012-7094-35-00128-4",
ISSN = "0012-7094 (print), 1547-7398 (electronic)",
ISSN-L = "0012-7094",
MRclass = "99-04",
MRnumber = "1545886",
bibdate = "Tue Oct 24 13:24:42 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Duke Mathematical Journal",
journal-URL = "http://projecteuclid.org/info/euclid.dmj",
}
@Article{Birkhoff:1935:NICa,
author = "G. D. Birkhoff and M. R. Hestenes",
title = "Natural Isoperimetric Conditions in the Calculus of
Variations",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "21",
number = "2",
pages = "99--102",
month = feb,
year = "1935",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.21.2.99",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Wed Oct 25 10:45:03 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/content/by/year",
}
@Article{Birkhoff:1935:NICb,
author = "G. D. Birkhoff and M. R. Hestenes",
title = "Natural Isoperimetric Conditions in the Calculus of
Variations",
journal = j-DUKE-MATH-J,
volume = "1",
number = "2",
month = jun,
year = "1935",
CODEN = "DUMJAO",
DOI = "https://doi.org/10.1215/s0012-7094-35-00118-1",
ISSN = "0012-7094 (print), 1547-7398 (electronic)",
ISSN-L = "0012-7094",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
author-dates = "Garrett Birkhoff (19 January 1911--22 November 1996);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Duke Mathematical Journal",
journal-URL = "http://projecteuclid.org/info/euclid.dmj",
}
@Article{Hestenes:1936:MPF,
author = "M. R. Hestenes",
title = "Minimax Principle for Functions",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "22",
number = "2",
pages = "115--119",
month = feb,
year = "1936",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.22.2.115",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.pnas.org/doi/10.1073/pnas.22.2.115",
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/content/by/year",
}
@Article{Hestenes:1936:PBC,
author = "Magnus R. Hestenes",
title = "The problem of {Bolza} in the calculus of variations
in parametric form",
journal = j-AM-J-MATH,
volume = "58",
number = "2",
pages = "391--406",
month = apr,
year = "1936",
CODEN = "AJMAAN",
DOI = "https://doi.org/10.2307/2371048",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0014.11803",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "American Journal of Mathematics",
journal-URL = "https://www.jstor.org/journal/amerjmath",
ZBmath = "3021921",
}
@Article{Hestenes:1936:SCP,
author = "Magnus R. Hestenes",
title = "On sufficient conditions in the problems of {Lagrange}
and {Bolza}",
journal = j-ANN-MATH-2,
volume = "37",
number = "3",
pages = "543--551",
month = jul,
year = "1936",
CODEN = "ANMAAH",
DOI = "https://doi.org/10.2307/1968477",
ISSN = "0003-486x (print), 1939-8980 (electronic)",
ISSN-L = "0003-486X",
MRclass = "99-04",
MRnumber = "1503298",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0015.02603",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Annals of Mathematics. Second Series",
journal-URL = "http://www.jstor.org/action/showPublication?journalCode=annamath",
ZBmath = "3023272",
}
@Article{Hestenes:1937:DSP,
author = "Magnus R. Hestenes",
title = "A direct sufficiency proof for the problem of {Bolza}
in the calculus of variations",
journal = j-TRANS-AM-MATH-SOC,
volume = "42",
number = "1",
pages = "141--154",
month = jul,
year = "1937",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1989678",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "49K05",
MRnumber = "1501917",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0017.26801",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ZBmath = "3027706",
}
@Article{Hestenes:1938:SPI,
author = "M. H. Hestenes",
title = "A sufficiency proof for isoperimetric problems in the
calculus of variations",
journal = j-BULL-AMS,
volume = "44",
number = "10",
pages = "662--667",
month = oct,
year = "1938",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1934-05855-5",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Wed Oct 25 11:08:07 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1938-44-10/S0002-9904-1938-06838-3/",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@Article{Hestenes:1939:GPB,
author = "M. R. Hestenes",
title = "Generalized problem of {Bolza} in the calculus of
variations",
journal = j-DUKE-MATH-J,
volume = "5",
number = "2",
pages = "309--324",
month = jun,
year = "1939",
CODEN = "DUMJAO",
DOI = "https://doi.org/10.1215/s0012-7094-39-00528-4",
ISSN = "0012-7094 (print), 1547-7398 (electronic)",
ISSN-L = "0012-7094",
bibdate = "Wed Oct 25 11:13:39 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Duke Mathematical Journal",
journal-URL = "http://projecteuclid.org/info/euclid.dmj",
}
@Article{Hestenes:1939:NWC,
author = "M. R. Hestenes and W. T. Reid",
title = "A note on the {Weierstrass} condition in the calculus
of variations",
journal = j-BULL-AMS,
volume = "45",
number = "6",
pages = "471--473",
month = jun,
year = "1939",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1939-07015-8",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
MRclass = "99-04",
MRnumber = "1564006",
bibdate = "Wed Oct 25 11:17:15 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@Article{Hestenes:1940:TQF,
author = "M. R. Hestenes and E. J. McShane",
title = "A theorem on quadratic forms and its application in
the calculus of variations",
journal = j-TRANS-AM-MATH-SOC,
volume = "47",
number = "3",
pages = "501--512",
month = may,
year = "1940",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1989966",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "15.0X",
MRnumber = "2839",
MRreviewer = "W. T. Reid",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
}
@Article{Hestenes:1941:AGT,
author = "Magnus R. Hestenes",
title = "An analogue of {Green}'s theorem in the calculus of
variations",
journal = j-DUKE-MATH-J,
volume = "8",
number = "2",
pages = "300--311",
month = jun,
year = "1941",
CODEN = "DUMJAO",
DOI = "https://doi.org/10.1215/S0012-7094-41-00823-2",
ISSN = "0012-7094 (print), 1547-7398 (electronic)",
ISSN-L = "0012-7094",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0025.18103",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Duke Mathematical Journal",
journal-URL = "http://projecteuclid.org/info/euclid.dmj",
received = "21 November 1940; revised 29 January 1941; presented
15 April 1939 as \booktitle{On the first necessary
condition for minima of double integrals}.",
ZBmath = "3040345",
}
@Article{Hestenes:1941:ERD,
author = "M. R. Hestenes",
title = "Extension of the range of a differentiable function",
journal = j-DUKE-MATH-J,
volume = "8",
number = "1",
pages = "183--192",
month = mar,
year = "1941",
CODEN = "DUMJAO",
DOI = "https://doi.org/10.1215/s0012-7094-41-00812-8",
ISSN = "0012-7094 (print), 1547-7398 (electronic)",
ISSN-L = "0012-7094",
bibdate = "Wed Oct 25 11:20:44 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Duke Mathematical Journal",
journal-URL = "http://projecteuclid.org/info/euclid.dmj",
received = "21 November 1940",
}
@Article{Hestenes:1942:PBC,
author = "M. R. Hestenes",
title = "The problem of {Bolza} in the calculus of variations",
journal = j-BULL-AMS,
volume = "48",
number = "2",
pages = "57--75",
month = feb,
year = "1942",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/S0002-9904-1942-07600-2",
ISSN = "0002-9904 (print), 1936-881x (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/bull/1942-48-02/S0002-9904-1942-07600-2/S0002-9904-1942-07600-2.pdf",
ZMnumber = "0063.02000",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
remark = "Presented 11 April 1941.",
ZBmath = "3104795",
}
@Article{Hestenes:1945:TCP,
author = "Magnus R. Hestenes",
title = "A theory of critical points",
journal = j-AM-J-MATH,
volume = "67",
number = "4",
pages = "521--562",
month = oct,
year = "1945",
CODEN = "AJMAAN",
DOI = "https://doi.org/10.2307/2371978",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
MRclass = "56.0X",
MRnumber = "13911",
MRreviewer = "M. Shiffman",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0061.41109",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "American Journal of Mathematics",
journal-URL = "https://www.jstor.org/journal/amerjmath",
ZBmath = "3102296",
}
@Article{Hestenes:1946:SCI,
author = "Magnus R. Hestenes",
title = "Sufficient conditions for the isoperimetric problem of
{Bolza} in the calculus of variations",
journal = j-TRANS-AM-MATH-SOC,
volume = "60",
number = "1",
pages = "93--118",
month = jul,
year = "1946",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1990244",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0063.02003",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ZBmath = "3104798",
}
@Article{Hestenes:1946:TLC,
author = "Magnus R. Hestenes",
title = "Theorem of {Lindeberg} in the calculus of variations",
journal = j-TRANS-AM-MATH-SOC,
volume = "60",
number = "1",
pages = "72--92",
month = jul,
year = "1946",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1990243",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0063.02002",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ZBmath = "3104797",
}
@Article{Hestenes:1946:WFC,
author = "Magnus R. Hestenes",
title = "The {Weierstrass} {$E$}-function in the calculus of
variations",
journal = j-TRANS-AM-MATH-SOC,
volume = "60",
number = "1",
pages = "51--71",
month = jul,
year = "1946",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1990242",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0063.02001",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ZBmath = "3104796",
}
@Article{Hestenes:1947:ASP,
author = "Magnus R. Hestenes",
title = "An alternate sufficiency proof for the normal problem
of {Bolza}",
journal = j-TRANS-AM-MATH-SOC,
volume = "61",
number = "2",
pages = "256--264",
month = mar,
year = "1947",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1990219",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0038.26302",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ZBmath = "3058202",
}
@Article{Hestenes:1947:ISP,
author = "Magnus R. Hestenes",
title = "An indirect sufficiency proof for the problem of
{Bolza} in nonparametric form",
journal = j-TRANS-AM-MATH-SOC,
volume = "62",
number = "3",
pages = "509--535",
month = nov,
year = "1947",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1990468",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "49.0X",
MRnumber = "23465",
MRreviewer = "H. H. Goldstine",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0032.02004",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ZBmath = "3049271",
}
@Article{Hestenes:1948:SCM,
author = "Magnus R. Hestenes",
title = "Sufficient conditions for multiple integral problems
in the calculus of variations",
journal = j-AM-J-MATH,
volume = "70",
number = "2",
pages = "239--276",
month = apr,
year = "1948",
CODEN = "AJMAAN",
DOI = "https://doi.org/10.2307/2372325",
ISSN = "0002-9327 (print), 1080-6377 (electronic)",
ISSN-L = "0002-9327",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0036.07201",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "American Journal of Mathematics",
journal-URL = "https://www.jstor.org/journal/amerjmath",
ZBmath = "3054804",
}
@TechReport{Hestenes:1949:NMO,
author = "Magnus Rudolph Hestenes",
title = "Numerical Methods of Obtaining Solutions of Fixed
Endpoint Problems in the Calculus of Variations",
type = "Research Memorandum",
number = "RM-0102-PR",
institution = "The RAND Corporation",
address = "Santa Monica, CA, USA",
pages = "17",
year = "1949",
bibdate = "Wed Oct 25 11:28:09 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.rand.org/pubs/research_memoranda/RM0102.html",
abstract = "A generalization of the method of Newton for functions
of a single real variable $x$. The method presented
computes arcs which satisfy the Euler equations of an
integral subject to certain boundary conditions.",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Hestenes:1950:EIC,
author = "Magnus R. Hestenes",
title = "An Elementary Introduction to the Calculus of
Variations",
journal = j-MATH-MAG,
volume = "23",
number = "5",
pages = "249--267",
month = may # "\slash " # jun,
year = "1950",
CODEN = "MAMGA8",
ISSN = "0025-570X (print), 1930-0980 (electronic)",
ISSN-L = "0025-570X",
bibdate = "Tue Oct 24 13:52:14 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.jstor.org/stable/pdf/3028990.pdf",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
}
@TechReport{Hestenes:1950:GPC,
author = "Magnus Rudolph Hestenes",
title = "A General Problem in the Calculus of Variations with
Applications to the Paths of Least Time",
type = "Research Memorandum",
number = "RM-100",
institution = "The RAND Corporation",
address = "Santa Monica, CA, USA",
pages = "i + 45",
day = "1",
month = mar,
year = "1950",
bibdate = "Tue Oct 24 13:10:57 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.rand.org/pubs/research_memoranda/RM100.html",
abstract = "The present paper is concerned with paths of least
time for an airplane. This problem when formulated
analytically leads us to a problem in the calculus of
variations of a type which has not been adequately
treated in the literature. However, the problem can be
transformed into a problem, commonly called the problem
of Bolza. The purpose of the present paper is to
collect known results for the problem of Bolza and
interpret them in terms of the new problem here
formulated. This is done in Sections 2, 3, 4 and 5. In
sections 10 and 11 we treat the case when additional
constraints are imposed. Applications to paths of least
time are found in Sections 8, 9 and 11.\par
The derivation of the results on the problem of Bolza
which we have used can be found in a book by G. A.
Bliss entitled ``\booktitle{Lectures on the Calculus of
Variations}'', The University of Chicago Press. The
results given by Bliss are stated in a somewhat
different form than those here given. They are however
equivalent and are related by the transformation given
by Bliss in the introductory sections on the problem of
Bolza.",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Forsythe:1951:IMS,
author = "George E. Forsythe and Magnus R. Hestenes and J.
Barkley Rosser",
title = "Iterative methods for solving linear equations",
journal = j-BULL-AMS,
volume = "57",
number = "6",
pages = "480--480",
month = nov,
year = "1951",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Thu Nov 09 15:37:46 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib",
URL = "https://www.ams.org/journals/bull/1951-57-06/",
acknowledgement = ack-nhfb,
author-dates = "George Elmer Forsythe (8 January 1917--9 April 1972);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
remark = "One-paragraph abstract only. The survey paper by Gene
H. Golub and Dianne P. O'Leary, ``Some History of the
Conjugate Gradient and {Lanczos} Algorithms:
1948--1976'', SIAM Review {\bf 31}(1) 50--102 March
1989, doi:10.1137/1031003, (entry Golub:1989:SHC in
golub-gene-h.bib) credits this paper as one of two
precursors to the conjugate gradient method that was
later, and independently, developed in depth in 1951 by
Eduard Stiefel and Magnus Hestenes and published in
their joint paper, ``Methods of Conjugate Gradients for
Solving Linear Systems'' Journal of Research of the
National Bureau of Standards {\bf 49}(6) 409--436
December 1952, doi:10.6028/jres.049.044 (entry
Hestenes:1952:MCG in hestenes-magnus-r.bib and
stiefel-eduard.bib).",
}
@Article{Hestenes:1951:ATQ,
author = "Magnus R. Hestenes",
title = "Applications of the theory of quadratic forms in
{Hilbert} space to the calculus of variations",
journal = j-PAC-J-MATH,
volume = "1",
number = "4",
pages = "525--581",
month = dec,
year = "1951",
CODEN = "PJMAAI",
DOI = "https://doi.org/10.2140/pjm.1951.1.525",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
MRclass = "49.0X",
MRnumber = "46590",
MRreviewer = "L. M. Graves",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
note = "Entry \cite{Miele:1974:APM} says this is perhaps
Hestenes's best known paper, although the conjugate
gradient paper \cite{Hestenes:1952:MCG} is also highly
cited.",
URL = "http://projecteuclid.org/euclid.pjm/1103052021",
ZMnumber = "0045.20806",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
ZBmath = "3070068",
}
@TechReport{Hestenes:1951:IMS,
author = "Magnus R. Hestenes",
title = "Iterative Methods for Solving Linear Equations",
type = "NAML Report",
number = "52-9",
institution = "National Bureau of Standards",
address = "Los Angeles, CA, USA",
day = "2",
month = jul,
year = "1951",
bibdate = "Fri Nov 10 06:08:52 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
remark = "Superceded by \cite{Hestenes:1952:MCG}. Reprinted in
\cite{Hestenes:1973:IMS}.",
}
@Article{Hestenes:1951:MGC,
author = "Magnus R. Hestenes and William Karush",
title = "A method of gradients for the calculation of the
characteristic roots and vectors of a real symmetric
matrix",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "47",
number = "1",
pages = "45--61",
month = jul,
year = "1951",
DOI = "https://doi.org/10.6028/jres.047.008",
ISSN = "0091-0635",
bibdate = "Wed Oct 25 11:34:44 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
received = "4 May 1950",
}
@Article{Hestenes:1951:S,
author = "M. R. Hestenes and W. Karush",
title = "Solutions of {$ A x = \lambda B x $}",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "47",
number = "6",
pages = "471--478",
month = dec,
year = "1951",
DOI = "https://doi.org/10.6028/jres.047.056",
ISSN = "0091-0635",
bibdate = "Wed Oct 25 11:39:00 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
note = "Research paper 2275.",
abstract = "The problem is to determine characteristic numbers and
vectors for the problem $ A x = \lambda B x $, where
$A$, $B$ are $ n \times n$ Hermitian matrices. A
generalized gradient $ \eta $ is defined. From a first
approximation $ x_0$, a second approximation $ x_1 =
x_0 + \alpha \eta $ is determined. Successive
approximations, with appropriate alphas, converge to a
solution",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
received = "11 September 1950",
}
@TechReport{Hestenes:1951:SLE,
author = "Magnus R. Hestenes and Marvin L. Stein",
title = "The Solution of Linear Equations by Minimization",
type = "NAML Report",
number = "52-45",
institution = "National Bureau of Standards",
address = "Los Angeles, CA, USA",
day = "12",
month = dec,
year = "1951",
bibdate = "Fri Nov 10 06:12:47 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Rosser:1951:SCE,
author = "J. B. Rosser and C. Lanczos and M. R. Hestenes and W.
Karush",
title = "Separation of close eigenvalues of a real symmetric
matrix",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "47",
number = "4",
pages = "291--297",
month = oct,
year = "1951",
DOI = "https://doi.org/10.6028/jres.047.037",
ISSN = "0091-0635 (print), 2376-5305 (electronic)",
ISSN-L = "0091-0635",
MRclass = "65.0X",
MRnumber = "0048914 (14,92d)",
MRreviewer = "G. E. Forsythe",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Research Paper 2256.",
abstract = "In order to test two methods, one proposed by C.
Lanczos and the other by M. R. Hestenes and W. Karush,
for the numerical calculation of eigenvalues of
symmetric matrices, an 8 by 8 matrix is constructed
that has several sets of eigenvalues close together.
The application of the two methods to this test matrix
is described, and in addition, a third method for
dealing with such problems is proposed.",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
}
@Article{Hestenes:1952:MCG,
author = "Magnus R. Hestenes and Eduard Stiefel",
title = "Methods of Conjugate Gradients for Solving Linear
Systems",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "49",
number = "6",
pages = "409--436",
month = dec,
year = "1952",
DOI = "https://doi.org/10.6028/jres.049.044",
ISSN = "0091-0635 (print), 2376-5305 (electronic)",
ISSN-L = "0091-0635",
MRclass = "65.0X",
MRnumber = "0060307",
MRreviewer = "A. S. Householder",
bibdate = "Wed Sep 2 16:23:13 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib",
note = "Research paper 2379.",
ZMnumber = "0048.09901",
abstract = "An iterative algorithm is given for solving a system $
A x = k $ of $n$ linear equations in $n$ unknowns. The
solution is given in $n$ steps. It is shown that this
method is a special case of a very general method which
also includes Gaussian elimination. These general
algorithms are essentially algorithms for finding an
$n$ dimensional ellipsoid. Connections are made with
the theory of orthogonal polynomials and continued
fractions.",
acknowledgement = ack-nhfb,
ajournal = "J. Research Nat. Bur. Standards",
author-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
received = "8 May 1952",
remark = "This is the paper that introduced conjugate gradient
methods, which remain in wide use in numeric
computation, with many algorithmic enhancements. The
MathSciNet database lists over 1700 publications about
conjugate gradients.",
ZBmath = "3075195",
}
@InProceedings{Hestenes:1953:DEE,
author = "Magnus R. Hestenes",
title = "Determination of eigenvalues and eigenvectors of
matrices",
crossref = "Paige:1953:SLE",
pages = "89--94",
year = "1953",
bibdate = "Tue Oct 24 14:05:56 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0052.35002",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
ZBmath = "3083850",
}
@InProceedings{Hestenes:1954:HSM,
author = "Magnus R. Hestenes",
editor = "J. Gerretsen and J. {De Groot}",
booktitle = "{Proceedings of the International Congress of
Mathematicians 1954. Amsterdam, September 2--9. Vol.
III. Stated addresses in sections. Symposia}",
title = "{Hilbert} space methods in variational theory and
numerical analysis",
volume = "3",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "229--236",
year = "1954",
bibdate = "Tue Oct 24 11:47:31 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0073.32203",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
xxyear = "1956",
ZBmath = "3122636",
}
@Article{Hestenes:1955:ICM,
author = "Magnus R. Hestenes",
title = "Iterative computational methods",
journal = j-COMM-PURE-APPL-MATH,
volume = "8",
number = "1",
pages = "85--96",
month = feb,
year = "1955",
CODEN = "CPAMAT, CPMAMV",
DOI = "https://doi.org/10.1002/cpa.3160080106",
ISSN = "0010-3640 (print), 1097-0312 (electronic)",
ISSN-L = "0010-3640",
MRclass = "65-XX",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0066.10201",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Communications on Pure and Applied Mathematics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
ZBmath = "3112207",
}
@InProceedings{Hestenes:1956:CGM,
author = "Magnus R. Hestenes",
booktitle = "{Proceedings of Symposia in Applied Mathematics. Vol.
VI, Numerical analysis}",
title = "The Conjugate Gradient Method for Solving Linear
Systems",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "83--102",
year = "1956",
MRclass = "65.3X",
MRnumber = "84178",
MRreviewer = "E. Stiefel",
bibdate = "Wed May 4 18:52:09 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/subjects/domain-decomp.bib",
ZMnumber = "0072.14102",
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
ZBmath = "3120437",
}
@InCollection{Hestenes:1956:ECV,
author = "Magnus R. Hestenes",
title = "Elements of the Calculus of Variations",
crossref = "Beckenbach:1956:MME",
chapter = "4",
pages = "??--??",
year = "1956",
bibdate = "Tue Oct 24 14:20:07 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
tableofcontents = "4.1 Introduction \\
4.2 Some Elementary Variational Problems \\
4.3 General Statements of Problems; Necessary
Conditions for a Minimum \\
4.4 Derivation of the Euler Equations \\
4.5 Special Cases \\
4.6 Integrands of the Form $f(x, y)$ \\
4.7 Hamilton's Principle \\
4.8 Hamiltonians \\
4.9 Isoperimetric Problems \\
4.10 Variable End-point Problems \\
4.11 Minima of Functions of Integrals \\
4.12 Problem of Bolza \\
4.13 Multiple-integral Problems",
}
@Article{Hestenes:1958:IMB,
author = "Magnus R. Hestenes",
title = "Inversion of Matrices by Biorthogonalization and
Related Results",
journal = j-J-SIAM,
volume = "6",
number = "1",
pages = "51--90",
month = mar,
year = "1958",
CODEN = "JSIMAV",
DOI = "https://doi.org/10.1137/0106005",
ISSN = "0368-4245 (print), 1095-712X (electronic)",
MRclass = "65.3X",
MRnumber = "92215",
MRreviewer = "A. S. Householder",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/siam.bib; JSTOR
database",
ZMnumber = "0085.33003",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of the Society for Industrial and Applied
Mathematics",
journal-URL = "http://epubs.siam.org/loi/smjmap.1",
ZBmath = "3139991",
}
@Article{Hestenes:1961:QVT,
author = "Magnus R. Hestenes",
title = "Quadratic variational theory and linear elliptic
partial differential equations",
journal = j-TRANS-AM-MATH-SOC,
volume = "101",
number = "2",
pages = "306--350",
month = nov,
year = "1961",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1993376",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "35.04 (35.43)",
MRnumber = "133575",
MRreviewer = "K. Maurin",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0103.06703",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
ZBmath = "3168005",
}
@Article{Hestenes:1961:RHM,
author = "M. R. Hestenes",
title = "Relative {Hermitian} matrices",
journal = j-PAC-J-MATH,
volume = "11",
number = "1",
pages = "225--245",
month = mar,
year = "1961",
CODEN = "PJMAAI",
DOI = "https://doi.org/10.2140/pjm.1961.11.225",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0109.24702",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
ZBmath = "3178662",
}
@Article{Hestenes:1961:RSA,
author = "Magnus R. Hestenes",
title = "Relative self-adjoint operators in {Hilbert} space",
journal = j-PAC-J-MATH,
volume = "11",
number = "4",
pages = "1315--1357",
month = dec,
year = "1961",
CODEN = "PJMAAI",
DOI = "https://doi.org/10.2140/pjm.1961.11.1315",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
MRclass = "47.40",
MRnumber = "136996",
MRreviewer = "D. C. Kleinecke",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "http://projecteuclid.org/euclid.pjm/1103036917",
ZMnumber = "0171.34601",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
ZBmath = "3273404",
}
@InCollection{Hestenes:1962:I,
author = "Magnus R. Hestenes",
title = "Introduction",
crossref = "Beckenbach:1962:MME",
pages = "????",
year = "1962",
bibdate = "Wed Oct 25 06:30:54 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Hestenes:1962:TAA,
author = "Magnus R. Hestenes",
title = "A Ternary Algebra with Applications to Matrices and
Linear Transformations",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "11",
number = "1",
pages = "138--195",
month = jan,
year = "1962",
CODEN = "AVRMAW",
DOI = "https://doi.org/10.1007/BF00253936",
ISSN = "0003-9527 (print), 1432-0673 (electronic)",
ISSN-L = "0003-9527",
bibdate = "Tue Oct 24 13:16:17 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://link.springer.com/article/10.1007/BF00253936",
ZMnumber = "0201.37001",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Archive for Rational Mechanics and Analysis",
journal-URL = "http://link.springer.com/journal/205",
xxpages = "138--194",
ZBmath = "3319632",
}
@InProceedings{Hestenes:1964:VTO,
author = "Magnus R. Hestenes",
editor = "A. V. Balakrishnan and Lucien W. Neustadt",
booktitle = "Computational Methods in Optimization Problems,
{Proceedings of a conference held at University of
California, Los Angeles, January 30--31, 1964}",
title = "Variational theory and optimal control theory",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
bookpages = "x + 327",
pages = "1--22",
year = "1964",
MRclass = "49-XX",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0143.12501",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
ZBmath = "3230613",
}
@Article{Hestenes:1965:VTO,
author = "Magnus R. Hestenes",
title = "On Variational Theory and Optimal Control Theory",
journal = j-J-SOC-IND-APPL-MATH-A-ON-CONTROL,
volume = "3",
number = "1",
pages = "23--48",
month = jan,
year = "1965",
CODEN = "JSMCAL",
DOI = "https://doi.org/10.1137/0303003",
ISSN = "0887-4603 (print), 2168-359X (electronic)",
ISSN-L = "0887-4603",
MRclass = "93.40 (49.00)",
MRnumber = "184763",
MRreviewer = "G. M. Ewing",
bibdate = "Sun Mar 30 08:21:27 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/siamjcontrol.bib",
ZMnumber = "0151.12803",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "SIAM Journal on Control",
journal-URL = "http://epubs.siam.org/journal/sjcodc",
onlinedate = "January 1965",
ZBmath = "3242536",
}
@Book{Hestenes:1966:CVO,
author = "Magnus R. Hestenes",
title = "Calculus of Variations and Optimal Control Theory",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xii + 405",
year = "1966",
ISBN = "0-471-37470-9",
ISBN-13 = "978-0-471-37470-1",
bibdate = "Tue Oct 24 11:14:01 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0173.35703",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
tableofcontents = "1: Auxiliary Theorems, Maxima and Minima of
Functions of $n$-Variables / 1 \\
2: Classical Fixed Endpoint Problems / 53 \\
3: The Jacobi Condition, Field Theory, and Sufficiency
Conditions / 118 \\
4: A Generalized Multiplier Rule / 167 \\
5: Alternate Elementary Variational Problems / 202 \\
6: A General Fixed Endpoint Problem / 250 \\
7: Optimal Control Problems and the Problems of Mayer /
296 \\
8: Control Problems with Bounded State Variables / 352
\\
Appendix Embedding Theorems for Differential Equations
/ 375 \\
Bibliography / 401 \\
Index / 403",
ZBmath = "3276736",
}
@InProceedings{Hestenes:1966:ECV,
author = "M. R. Hestenes",
editor = "J. Barkley Rosser",
booktitle = "Lectures in Applied Mathematics {VI}, Space
Mathematics. Part 2, {Proceedings of the Summer
Seminar, Ithaca, New York, 1963}",
title = "Elements of calculus of variations and optimum control
theory",
volume = "6",
publisher = pub-AMS,
address = pub-AMS:adr,
bookpages = "v + 258",
pages = "212--254",
year = "1966",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
series = "Lectures in Applied Mathematics",
ZMnumber = "0148.08004",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
ZBmath = "3238887",
}
@Article{Hestenes:1968:ETD,
author = "M. R. Hestenes and T. Guinn",
title = "An embedding theorem for differential equations",
journal = j-J-OPT-THEORY-APPL,
volume = "2",
number = "2",
pages = "87--101",
month = mar,
year = "1968",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00929585",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0186.22703",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ZBmath = "3296865",
}
@Article{Hestenes:1968:PQF,
author = "Magnus R. Hestenes",
title = "Pairs of Quadratic Forms",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "1",
number = "3",
pages = "397--407",
month = jul,
year = "1968",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(68)90016-5",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Feb 17 11:44:01 MST 2016",
bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/linala1960.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0024379568900165",
ZMnumber = "0174.06401",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "la, geig, matrix pencil, symmetric matrix",
ZBmath = "3277609",
}
@InProceedings{Hestenes:1969:MGMa,
author = "M. R. Hestenes",
title = "Multiplier and gradient methods",
crossref = "Zadeh:1969:CMO",
pages = "143--163",
year = "1969",
MRclass = "90C30,65H05,49M30",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0208.18402",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
ZBmath = "3331230",
}
@Article{Hestenes:1969:MGMb,
author = "Magnus R. Hestenes",
title = "Multiplier and gradient methods",
journal = j-J-OPT-THEORY-APPL,
volume = "4",
number = "5",
pages = "303--320",
month = nov,
year = "1969",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00927673",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "49.20 (65.00) 65K10 49M15",
MRnumber = "271809",
MRreviewer = "P. J. Laurent",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0174.20705",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ZBmath = "3278014",
}
@InProceedings{Hestenes:1969:VTO,
author = "Magnus R. Hestenes",
title = "Variational Theory and Optimal Control Theory",
crossref = "Zadeh:1969:CMO",
pages = "??--??",
year = "1969",
bibdate = "Tue Oct 24 14:03:13 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Hestenes:1973:IMS,
author = "M. R. Hestenes",
title = "Iterative methods for solving linear equations",
journal = j-J-OPT-THEORY-APPL,
volume = "11",
number = "4",
pages = "323--334",
month = apr,
year = "1973",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00932484",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "65F10",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0242.65035",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ZBmath = "3383461",
}
@Article{Hestenes:1973:SLE,
author = "M. R. Hestenes and M. L. Stein",
title = "The solution of linear equations by minimization",
journal = j-J-OPT-THEORY-APPL,
volume = "11",
number = "4",
pages = "335--359",
month = apr,
year = "1973",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00932485",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "65F30,65F10",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0242.65043",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ZBmath = "3383469",
}
@Article{Hestenes:1973:TA,
author = "Magnus R. Hestenes",
title = "On a ternary algebra",
journal = j-SCRIPTA-MATH,
volume = "29",
number = "3--4",
pages = "253--272",
year = "1973",
ISSN = "0036-9713",
MRclass = "20N10 (16A78) 08Axx 15A63",
MRnumber = "444827",
MRreviewer = "V. Havel",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
ZMnumber = "0275.20120",
acknowledgement = ack-nhfb,
ajournal = "Scripta Math.",
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to
the Philosophy, History, and Expository Treatment of
Mathematics",
remark = "This journal, published at Yeshiva University in New
York City, ceased with v29 n3--4 in 1973. I have been
yet unable to find any online repository of its
issues.",
ZBmath = "3432645",
}
@Article{Hestenes:1974:MCQa,
author = "Magnus Hestenes and Ray Redheffer",
title = "On the minimization of certain quadratic functionals.
{I}",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "56",
number = "1",
pages = "1--14",
month = mar,
year = "1974",
CODEN = "AVRMAW",
DOI = "https://doi.org/10.1007/BF00279818",
ISSN = "0003-9527 (print), 1432-0673 (electronic)",
ISSN-L = "0003-9527",
MRclass = "49A35 49J99",
MRnumber = "367755",
MRreviewer = "L. Miko\l ajczyk",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0311.49002",
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Archive for Rational Mechanics and Analysis",
journal-URL = "http://link.springer.com/journal/205",
ZBmath = "3486528",
}
@Article{Hestenes:1974:MCQb,
author = "Magnus Hestenes and Ray Redheffer",
title = "On the minimization of certain quadratic functionals.
{II}",
journal = j-ARCH-RAT-MECH-ANAL,
volume = "56",
number = "1",
pages = "15--33",
month = mar,
year = "1974",
CODEN = "AVRMAW",
DOI = "https://doi.org/10.1007/BF00279819",
ISSN = "0003-9527 (print), 1432-0673 (electronic)",
ISSN-L = "0003-9527",
MRclass = "49J99",
bibdate = "Tue Oct 24 17:43:20 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0311.49003",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Archive for Rational Mechanics and Analysis",
journal-URL = "http://link.springer.com/journal/205",
ZBmath = "3486529",
}
@Book{Hestenes:1975:OTF,
author = "Magnus R. Hestenes",
title = "Optimization Theory: The Finite Dimensional Case",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xiii + 447",
year = "1975",
ISBN = "0-471-37471-7 (hardcover)",
ISBN-13 = "978-0-471-37471-8 (hardcover)",
LCCN = "QA402.5 .H47",
MRclass = "90Cxx 90C05 90-02 90C30 90C25 49-02 49Mxx 65K05",
bibdate = "Tue Oct 24 11:17:00 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "",
ZMnumber = "0327.90015",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
shorttableofcontents = "1: Unconstrained and Linearly Constrained
Extrema / 1 \\
2: Applications to Matrices and Quadratic Forms / 85
\\
3: The Lagrange Multiplier Rule for Equality
Constraints / 138 \\
4: General Constrained Minimum Problems / 177 \\
5: Augmentability and Lagrange Multipliers / 253 \\
6: Images and Lagrange Multipliers / 313 \\
Appendix / 393 \\
Bibliography / 437 \\
Index / 445",
tableofcontents = "1: Unconstrained and Linearly Constrained Extrema /
1 \\
1. Preliminary remarks / 1 \\
2. Existence of extreme points / 2 \\
3. Unconstrained local minima and maxima / 11 \\
4. Positive symmetric matrices / 21 \\
5. Minima of convex functions / 27 \\
6. Linearly constrained local minima and maxima / 37
\\
7. Minima of quadratic functions / 46 \\
8. Inner product spaces and the Gram--Schmidt process /
57 \\
9. Eigenvalues and eigenvectors of a real symmetric
matrix / 70 \\
\\
2: Applications to Matrices and Quadratic Forms / 85
\\
1. Introduction / 835 \\
2. Relative eigenvalues and eigenvectors / 85 \\
3. Eigenvalues on subspaces / 94 \\
4. A fundamental lemma / 97 \\
5. Quadratic forms of arcs / 101 \\
6. Further properties of quadratic forms / 112 \\
7. Rectangular matrices, norms, and principal values /
118 \\
8. Pseudoinverses and *-reciprocals of matrices / 130
\\
\\
3: The Lagrange Multiplier Rule for Equality
Constraints / 138 \\
1. General remarks / 138 \\
2. Constrained minima / 139 \\
3. Sufficient conditions for a local constrained
minimum / 151 \\
4. Classification of critical points / 156 \\
5. Tangent vectors and normality / 161 \\
6. Gradient of a function relative to constraints / 167
\\
7. Implicit function theorems / 171 \\
\\
4: General Constrained Minimum Problems / 177 \\
1. Introduction / 177 \\
2. The Lagrange multiplier rule / 179 \\
3. Convex cones and their duals / 187 \\
4. Tangent cones and normal cones / 203 \\
5. Remarks on differentiation / 210 \\
6. Minimum of a function on an arbitrary set / 213 \\
7. Minima subject to nonlinear constraints / 221 \\
8. Concave and linear constraints / 230 \\
9. Linear programming / 234 \\
10. Criteria for regularity / 237 \\
11. Infinitely many inequality constraints / 245 \\
12. A simple integral problem / 249 \\
\\
5: Augmentability and Lagrange Multipliers / 253 \\
1. Introduction / 253 \\
2. Penalty functions / 255 \\
3. Removal of constraints / 263 \\
4. Augmentability and the Lagrange multiplier rule /
267 \\
5. Minima subject to simple inequality constraints /
273 \\
6. Augmentability in the case of inequality constraints
/ 281 \\
7. An extended Lagrange multiplier rule / 289 \\
8. Quasinormality / 296 \\
9. Extensions of earlier results / 302 \\
10. A method of multipliers / 307 \\
\\
6: Images and Lagrange Multipliers / 313 \\
1. Introduction / 313 \\
2. Illustrative examples / 315 \\
3. Convex programming / 324 \\
4. Convex programming with linear constraints / 335 \\
5. Further examples / 343 \\
6. Minima relative to general inequality constraints /
347 \\
7. Applications to quadratic forms / 354 \\
8. Implicit function theorems / 361 \\
9. Derived cones and derived sets / 364 \\
10. Minima relative to equality and inequality
constraints / 371 \\
11. Further theorems on tangent spaces and derived sets
/ 384 \\
12. Auxiliary theorems / 388 \\
\\
Appendix / 393 \\
1. Introduction / 393 \\
2. Euclidean $n$-space / 393 \\
3. Basic concepts / 406 \\
4. Extreme points of functions / 411 \\
5. Local minima and maxima--the one-variable case / 416
\\
6. Functions of class $C*$ / 427 \\
\\
Bibliography / 437 \\
\\
Index / 445",
ZBmath = "3513549",
}
@Article{Hestenes:1975:PCG,
author = "Magnus R. Hestenes",
title = "Pseudoinverses and Conjugate Gradients",
journal = j-CACM,
volume = "18",
number = "1",
pages = "40--43",
month = jan,
year = "1975",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/360569.360658",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65F20 15A09",
MRnumber = "51 2269",
MRreviewer = "G. Maess",
bibdate = "Mon Jan 22 06:49:43 MST 2001",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Hestenes75;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib",
note = "Collection of articles honoring {Alston S.
Householder}",
ZMnumber = "0304.65029",
abstract = "This paper is devoted to the study of connections
between pseudoinverses of matrices and conjugate
gradients and conjugate direction routines.",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)",
classification = "921",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "Communications of the ACM",
journal-URL = "https://dl.acm.org/loi/cacm",
journalabr = "Commun ACM",
keywords = "CG; conjugate direction routines; conjugate gradients;
ginv; Hermitian matrix; mathematical techniques;
matrices; matrix algebra; minimisation; minimization;
nla; pseudoinverse; pseudoinverses",
oldlabel = "Hestenes75",
treatment = "T Theoretical or Mathematical",
XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Hestenes75",
ZBmath = "3476478",
}
@Article{Hestenes:1975:QCP,
author = "M. R. Hestenes",
title = "Quadratic control problems",
journal = j-J-OPT-THEORY-APPL,
volume = "17",
number = "1--2",
pages = "1--42",
month = oct,
year = "1975",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00933915",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "90C20 49K27 46E20",
bibdate = "Tue Oct 24 17:42:28 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0292.49019",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ZBmath = "3457668",
}
@InProceedings{Hestenes:1976:QCP,
author = "Magnus R. Hestenes",
title = "On quadratic control problems",
crossref = "Russell:1976:CVC",
pages = "289--304",
year = "1976",
MRclass = "49-02 49Lxx 93B05",
bibdate = "Tue Oct 24 17:37:42 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0344.49003",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
ZBmath = "3536794",
}
@InProceedings{Hestenes:1976:RPA,
author = "Magnus R. Hestenes",
editor = "M. Zuhair Nashed",
booktitle = "Generalized Inverses and Applications. {Proceedings of
an Advanced Seminar sponsored by the Mathematics
Research Center at the University of Wisconsin,
Madison, Wisconsin, October 8--10, 1973}",
title = "A role of the pseudoinverse in analysis",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
bookpages = "xiv + 1054",
pages = "175--192",
year = "1976",
MRclass = "47A99 15A09 47A10 47A45 47A50 47B25",
bibdate = "Tue Oct 24 17:39:37 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
note = "Publication number 32.",
ZMnumber = "0342.47014",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
ZBmath = "3533581",
}
@InProceedings{Hestenes:1978:CDM,
author = "Magnus R. Hestenes",
editor = "J. Stoer",
booktitle = "Optimization Techniques. Part 1. {Proceedings of the
8th IFIP Conference on Optimization Techniques held in
W{\"u}rzburg, September 5--9, 1977}",
title = "Conjugate direction methods in optimization",
volume = "6",
publisher = pub-SV,
address = pub-SV:adr,
pages = "8--27",
year = "1978",
ISBN = "3-540-08707-9",
ISBN-13 = "978-3-540-08707-6",
MRclass = "90C20 90C30",
bibdate = "Tue Oct 24 17:35:32 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
series = "Lecture Notes in Control and Information Sciences",
ZMnumber = "0392.90064",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
ZBmath = "3609463",
}
@InProceedings{Hestenes:1978:SOP,
author = "Magnus R. Hestenes",
editor = "A. B. Schwarzkopf and Walter G. Kelley and Stanley B.
Eliason",
booktitle = "Optimal Control and Differential Equations.
{Proceedings of the Conference on Optimal Control and
Differential Equations held at the University of
Oklahoma, Norman, Oklahoma, March 24--27, 1977}",
title = "Solving optimization problems",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
bookpages = "xi + 335",
pages = "165--185",
year = "1978",
ISBN = "0-12-632250-3",
ISBN-13 = "978-0-12-632250-7",
MRclass = "65K05 90C52 90C30 65K10",
bibdate = "Tue Oct 24 17:32:02 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0451.65044",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
ZBmath = "3705807",
}
@Article{Hestenes:1980:AOT,
author = "M. R. Hestenes",
title = "Augmentability in optimization theory",
journal = j-J-OPT-THEORY-APPL,
volume = "32",
number = "4",
pages = "427--440",
month = dec,
year = "1980",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00934031",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "49M29",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0421.49033",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ZBmath = "3654898",
}
@Book{Hestenes:1980:CDM,
author = "Magnus R. Hestenes",
title = "Conjugate Direction Methods in Optimization",
volume = "12",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 325",
year = "1980",
ISBN = "0-387-90455-7 (New York), 3-540-90455-7 (Berlin)",
ISBN-13 = "978-0-387-90455-9 (New York), 978-3-540-90455-7
(Berlin)",
ISSN = "0172-4568",
MRclass = "65K10 49D 49M07 65F10 90C30 49-01 90C52 90C20",
bibdate = "Tue Oct 24 11:01:12 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
series = "Applications of Mathematics",
ZMnumber = "0439.49001",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
subject = "conjugate direction methods; numerical analysis;
m{\'e}thode des directions conjugu{\'e}es",
tableofcontents = "I: Newton's Method and the Gradient Method / 1 \\
I Introduction / 1 \\
2 Fundamental Concepts / 3 \\
3 Iterative Methods for Solving $g(x) = 0 $ / 14 \\
4 Convergence Theorems / 25 \\
5 Minimization of Functions by Newton's Method / 33 \\
6 Gradient Methods -- The Quadratic Case / 41 \\
7 General Descent Methods / 52 \\
8 Iterative Methods for Solving Linear Equations / 61
\\
9 Constrained Minima / 72 \\
\\
II: Conjugate Direction Methods / 81 \\
1 Introduction / 81 \\
2 Quadratic Functions on $\cal E^n$ / 82 \\
3 Basic Properties of Quadratic Functions / 90 \\
4 Minimization of a Quadratic Function $F$ on
$k$-Planes / 100 \\
5 Method of Conjugate Directions (cD-Method) / 108 \\
6 Method of Conjugate Gradients (CG-Algorithm) / 117
\\
7 Gradient PARTAN / 128 \\
8 CG-Algorithms for Nonquadratic Functions / 135 \\
9 Numerical Examples / 140 \\
10 Least Square Solutions / 147 \\
\\
III: Conjugate Gram--Schmidt Processes / 150 \\
1 Introduction / 150 \\
2 A Conjugate Gram--Schmidt Process / 151 \\
3 CGs-CG-Algorithms / 163 \\
4 A Connection of CGs-Algorithms with Gaussian
Elimination / 173 \\
5 Method of Parallel Displacements / 177 \\
6 Methods of Parallel Planes (PARP) / 184 \\
7 Modifications of Parallel Displacements Algorithms /
193 \\
8 CGs-Algorithms for Nonquadratic Functions / 199 \\
9 caGs-CG-Routines for Nonquadratic Functions / 207 \\
10 Gauss--Seidel CGs-Routines / 210 \\
11 The Case of Nonnegative Components / 212 \\
12 General Linear Inequality Constraints / 220 \\
\\
IV: Conjugate Gradient Algorithms / 231 \\
1 Introduction / 231 \\
2 Conjugate Gradient Algorithms / 232 \\
3 The Normalized CG-Algorithm / 241 \\
4 Termination / 247 \\
5 Clustered Eigenvalues / 252 \\
6 Nonnegative Hessians / 256 \\
7 A Planar CG-Algorithm / 259 \\
8 Justification of the Planar CG-Algorithm / 268 \\
9 Modifications of the CG-Algorithm / 273 \\
10 Two Examples / 283 \\
11 Connections between Generalized CG-Algorithms and
Standard CG- and cD-Algorithms / 290 \\
12 Least Square Solutions / 293 \\
13 Variable Metric Algorithms / 301 \\
14 A Planar CG-Algorithm for Nonquadratic Functions /
310 \\
\\
References / 319 \\
Index / 323",
ZBmath = "3686229",
}
@Book{Hestenes:1980:CVO,
author = "Magnus R. Hestenes",
title = "Calculus of Variations and Optimal Control Theory",
publisher = pub-R-E-KRIEGER,
address = pub-R-E-KRIEGER:adr,
pages = "xii + 405",
year = "1980",
ISBN = "0-471-37470-9",
ISBN-13 = "978-0-471-37470-1",
MRclass = "49-01 34H05 58E30 49J05 49J15 49J10 49J35 49J45 49K05
49K15 49K10 49K30 49K35 49L20 93B03 49R50 58E15 49Q20",
bibdate = "Tue Oct 24 11:14:01 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
note = "Reprint of \cite{Hestenes:1966:CVO}, with
corrections.",
series = "Applied Mathematics Series",
ZMnumber = "0481.49001",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
tableofcontents = "1: Auxiliary Theorems, Maxima and Minima of
Functions of $n$-Variables / 1 \\
2: Classical Fixed Endpoint Problems / 53 \\
3: The Jacobi Condition, Field Theory, and Sufficiency
Conditions / 118 \\
4: A Generalized Multiplier Rule / 167 \\
5: Alternate Elementary Variational Problems / 202 \\
6: A General Fixed Endpoint Problem / 250 \\
7: Optimal Control Problems and the Problems of Mayer /
296 \\
8: Control Problems with Bounded State Variables / 352
\\
Appendix Embedding Theorems for Differential Equations
/ 375 \\
Bibliography / 401 \\
Index / 403",
ZBmath = "3755326",
}
@Article{Hestenes:1983:SQV,
author = "M. R. Hestenes",
title = "Singular quadratic variational problems",
journal = j-J-OPT-THEORY-APPL,
volume = "41",
number = "1",
pages = "123--137",
month = sep,
year = "1983",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00934439",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "49J27,42C05,11E16,15A63,46C99",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0497.49009",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
ZBmath = "3783780",
}
@InProceedings{Hestenes:1987:CGV,
author = "M. R. Hestenes",
title = "Conjugacy and gradients in variational theory and
analysis",
crossref = "Crane:1987:HAC",
pages = "71--90",
year = "1987",
DOI = "https://doi.org/10.1145/41579.41586",
bibdate = "Fri Nov 17 09:56:16 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InCollection{Hestenes:1990:CG,
author = "Magnus R. Hestenes",
title = "Conjugacy and gradients",
crossref = "Nash:1990:HSC",
pages = "167--179",
year = "1990",
DOI = "https://doi.org/10.1145/87252.88084",
bibdate = "Fri Nov 16 11:10:53 MST 2012",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Manual{Hestenes:1991:NIN,
author = "Magnus R. Hestenes and John Todd",
title = "{NBS-INA}, the Institute for Numerical Analysis,
{UCLA} 1947--1954",
number = "730",
organization = pub-NTIS,
address = pub-NTIS:adr,
pages = "x + 198 (various)",
month = aug,
year = "1991",
LCCN = "QA76.95 .H47 1991; C 13.10: 730 Govt Pub; QA 297 H47
1991",
bibdate = "Wed Nov 3 09:30:14 MST 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
note = "Cover title: Mathematicians learning to use computers:
the Institute for Numerical Analysis, UCLA, 1947--1954.
Spine title: The Institute for Numerical Analysis,
UCLA, 1947--1954. Sponsored in part by the Mathematical
Association of America. Shipping list no.: 92-1306-M.",
series = "NIST Special Publication",
URL = "https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication730.pdf",
acknowledgement = ack-nhfb,
author-dates = "John Todd (16 May 1911--21 June 2007); Magnus Rudolf
Hestenes (13 February 1906--31 May 1991)",
keywords = "electronic digital computers --- research --- history;
Institute for Numerical Analysis (U.S.) --- history;
mathematics --- data processing --- history; numerical
analysis --- research --- history",
tableofcontents = "Foreword / iii \\
Preface / v \\
Chapter I \\
The Beginnings / 1 \\
The War Years --- 1939--1945 / 2 \\
The Post-War Years / 3 \\
Chapter II \\
The Period Summer 1947 through Summer 1948 / 7 \\
Chapter III \\
The Period Fall 1948 through Spring 1949 / 11 \\
Chapter IV \\
The Period Summer 1949 through Summer 1950 / 17 \\
Chapter V \\
The Period Fall 1950 through Spring 1951 / 23 \\
Chapter VI \\
The Period Summer 1951 through Spring 1952 / 27 \\
Chapter VII \\
The Period Summer 1952 through Spring 1953 / 33 \\
Chapter VIII \\
The Period Summer 1953 through Spring 1954 / 39 \\
Chapter IX \\
Some Typical Projects / 45 \\
Hilbert Matrices and Related Topics / 45 \\
Gerschgorin Theorems and Related Results / 47 \\
Solutions of Systems of Linear Equations / 48 \\
References / 67 \\
Photographs and Cartoons / 73 \\
Appendix A. John Hamilton Curtiss 1909--77 / A-1 \\
Appendix B. Two Papers by John H. Curtiss / B-1 \\
Appendix C. The SWAC [The National Bureau of Standards
Western Automatic Computer, by Harry D. Huskey] / C-1
\\
Appendix D. Symposia and Tables / D-1 \\
Appendix E. Educational Activities / E-1 \\
Appendix F. Personnel / F-1 \\
Index / ind-1",
}
@Book{Landesman:1991:LAA,
author = "Edward M. Landesman and Magnus Rudolph Hestenes",
title = "Linear Algebra: With Applications for Mathematics,
Science, and Engineering",
publisher = pub-PH,
address = pub-PH:adr,
year = "1991",
ISBN = "0-13-529561-0 (hardcover), 0-13-534967-2 (paperback)",
ISBN-13 = "978-0-13-529561-8 (hardcover), 978-0-13-534967-0
(paperback)",
LCCN = "QA184 .L364 1991",
MRclass = "15-01 15A18 15A04 65F05 65F15 15A15 15A03 15A63 65F10
00A06 15A06",
bibdate = "Tue Oct 24 11:36:24 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0752.15001",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
subject = "Algebras, Linear; Alg{\`e}bre lin{\'e}aire; Algebras,
Linear.",
tableofcontents = "1 Matrices: Basic Operations / 1 \\
1.0 Preliminaries / 2
\\
1.1 Introduction to Matrices / 7 \\
1.2 Addition, Subtraction, and Scalar Multiplication /
23 \\
1.3 Products of Matrices / 32 \\
1.4 The Transpose of a Matrix / 52 \\
1.5 An Interpretation of Matrix Products / 62 \\
1.6 Vectors and Their Geometric Interpretation / 71 \\
2 Inverses and Solutions of Linear Matrix Equations /
85 \\
2.1 Invertible Matrices / 86 \\
2.2 Elementary Matrices: Some Easily Invertible
Matrices / 100 \\
2.3 Construction of Inverses / 111 \\
2.4 Solutions of $A X = H$ for a General Matrix $A$ /
125 \\
3 Determinants and Their Properties / 147 \\
3.1 Determinants / 148 3.2 Properties of Determinants /
159 \\
3.3 Classical Adjoint and Cramer's Rule / 180 \\
3.4 Rank of a Matrix / 187 \\
4 Eigenvalues and Eigenvectors of a Square Matrix / 205
\\
4.1 Characteristic Polynomial and Eigenvalues of a
Square Matrix / 206 \\
4.2 Eigenvectors of a Square Matrix / 220 \\
4.3 Properties of Eigenvectors / 233 \\
4.4 Similarity of Matrices / 253 \\
4.5 Gerschgorin Intervals and Disks / 266 \\
4.6 Applications Involving Calculus / 273 \\
5 Linear Spaces / 283 \\
5.1 Linear Spaces and Subspaces / 284 \\
5.2 Generators and Bases of Linear Spaces / 298 \\
5.3 Basis Operators and Changes of Bases / 310 \\
5.4 Orthogonal Bases and the Gram--Schmidt Process in
$\mathbb{R}^n$ / ??? \\
6 Linear Transformations and Their Properties / 331 \\
6.1 Linear Transformations and Linear Operators / 332
\\
6.2 The Null Space and the Range of a Linear
Transformation / 344 \\
6.3 Applications to Matrices and Linear Equations / 360
\\
6.4 Orthogonal Projections / 368 \\
6.5 Orthogonal Matrices and Elementary Orthogonal
Matrices / 375 \\
6.6 Least Square Solutions / 388 \\
6.7 Pseudoinverses and Related Topics / 395 \\
6.8 Invariant Subspaces and Canonical Forms / 416 \\
7 Quadratic Forms and Geometric Applications / 431 \\
7.1 Quadratic Forms and Symmetric Matrices / 432 \\
7.2 Rayleigh Quotients / 443 \\
7.3 Quadratic Functions and Ellipsoids / 448 \\
8 Solving Linear Equations and Finding Eigenvalues /
459 \\
8.1 an Alternative Elimination Process / 460 \\
8.2 Elimination in the Symmetric Case / 470 \\
83 a Conjugate Gradient Routine / 476 \\
8.4 Gauss--Seidel Methods / 486 \\
8.5 The Power Method for Finding a Dominant Eigenvalue
/ 494 \\
Appendix I: Polynomials / 501 \\
Index / 513",
ZBmath = "53167",
}
@InCollection{Hestenes:2013:ECV,
author = "Magnus R. Hestenes",
title = "Elements of the Calculus of Variations",
crossref = "Beckenbach:2013:MMEa",
chapter = "4",
pages = "??--??",
year = "2013",
bibdate = "Tue Oct 24 14:20:07 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
tableofcontents = "4.1 Introduction \\
4.2 Some Elementary Variational Problems \\
4.3 General Statements of Problems; Necessary
Conditions for a Minimum \\
4.4 Derivation of the Euler Equations \\
4.5 Special Cases \\
4.6 Integrands of the Form $f(x, y)$ \\
4.7 Hamilton's Principle \\
4.8 Hamiltonians \\
4.9 Isoperimetric Problems \\
4.10 Variable End-point Problems \\
4.11 Minima of Functions of Integrals \\
4.12 Problem of Bolza \\
4.13 Multiple-integral Problems",
}
@InCollection{Hestenes:2013:I,
author = "Magnus R. Hestenes",
title = "Introduction",
crossref = "Beckenbach:2013:MMEb",
pages = "????",
year = "1962",
bibdate = "Wed Oct 25 06:30:54 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Bolza:1901:NPT,
author = "Oskar Bolza",
title = "New proof of a theorem of {Osgood}'s in the calculus
of variations",
journal = j-TRANS-AM-MATH-SOC,
volume = "2",
number = "4",
pages = "422--427",
month = oct,
year = "1901",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1986255",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "49J05",
MRnumber = "1500577",
bibdate = "Tue Oct 24 13:24:42 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://en.wikipedia.org/wiki/Oskar_Bolza",
acknowledgement = ack-nhfb,
author-dates = "Oskar Bolza (12 May 1857--5 July 1942)",
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
remark = "This is the paper with Bolza's problem that Hestenes
addresses in \cite{Bliss:1933:NPB, Hestenes:1933:SCPa,
Hestenes:1933:SCPb, Hestenes:1933:SCPc,
Hestenes:1934:BTP, Hestenes:1934:SCPa,
Hestenes:1934:SCPb, Hestenes:1936:PBC,
Hestenes:1936:SCP, Hestenes:1937:DSP,
Hestenes:1939:GPB, Hestenes:1942:PBC,
Hestenes:1946:SCI, Hestenes:1947:ASP,
Hestenes:1947:ISP, Hestenes:1950:GPC,
Hestenes:1956:ECV, Hestenes:2016:ECV}.",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Fox:1948:NSA,
author = "L. Fox and H. D. Huskey and J. H. Wilkinson",
title = "Notes on the solution of algebraic linear simultaneous
equations",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "1",
pages = "149--173",
year = "1948",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/1.1.149",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.0X",
MRnumber = "MR0026421 (10,152i)",
MRreviewer = "E. Bodewig",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
abstract = "In this paper four methods of solving simultaneous
equations and inverting matrices are described from the
viewpoint of the practical computer. The first three
methods can be performed on ordinary desk calculating
machines; the fourth uses Hollerith punched card
equipment. The desk methods considered are the method
of elimination or pivotal condensation, the method of
orthogonal vectors, and the method of Choleski. The
elimination method is, with slight variants, the simple
method taught at school, used in such a way that
solutions are obtained with the maximum possible speed
and accuracy. In the method of orthogonal vectors,
applicable only to symmetric matrices, a new set of
variables is chosen in such a way that the matrix is
transformed to a diagonal form, from which the solution
of equations or the inverse of the matrix is
immediately obtainable. The Choleski method, applied
here again only to symmetric matrices, expresses the
square matrix as the product of two triangular
matrices, the reciprocation of which is a relatively
simple operation. This method is quicker and more
accurate than the others and can be used, with slight
modifications, in the case of unsymmetric matrices. The
procedure used with punched card equipment is
essentially a mechanization of the elimination method,
with a considerable advantage in speed over the
corresponding desk method.",
acknowledgement = ack-nhfb,
author-dates = "James H. Wilkinson (27 September 1919--5 October
1986)",
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
remark = "The survey paper by Gene H. Golub and Dianne P.
O'Leary, ``Some History of the Conjugate Gradient and
{Lanczos} Algorithms: 1948--1976'', SIAM Review {\bf
31}(1) 50--102 March 1989, doi:10.1137/1031003, (entry
Golub:1989:SHC in golub-gene-h.bib) credits this paper
as the origin of the conjugate gradient method that was
later, and independently, developed in depth in 1951 by
Eduard Stiefel and Magnus Hestenes and published in
their joint paper, ``Methods of Conjugate Gradients for
Solving Linear Systems'' Journal of Research of the
National Bureau of Standards {\bf 49}(6) 409--436
December 1952, doi:10.6028/jres.049.044 (entry
Hestenes:1952:MCG in hestenes-magnus-r.bib and
stiefel-eduard.bib).",
}
@Article{Maehly:1954:IAA,
author = "Hans J. Maehly",
title = "{Zur iterativen Aufl{\"o}sung algebraischer
Gleichungen}. ({German}) [{On} the iterative solution
of algebraic equations]",
journal = j-Z-ANGE-MATH-PHYS,
volume = "5",
number = "3",
pages = "260--263",
month = may,
year = "1954",
CODEN = "ZAMPDB",
DOI = "https://doi.org/10.1007/bf01600333",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
bibdate = "Wed Oct 25 12:45:29 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
abstract = "The slow convergence of Newton's method for the
iterative approximation of the roots of an algebraic
equation may be improved by using a formula due to
Laguerre. It is shown that this formula together with
certain generalizations are useful for the numerical
calculation of both real and complex zeros. A method is
also given for the calculation of a further root of an
equation after several roots have already been found,
such that errors on the determination of the previous
roots will not affect the accuracy with which the
present one may be approximated",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik
= Journal of Applied Mathematics and Physics}",
journal-URL = "http://link.springer.com/journal/33",
received = "21 January 1954",
remark = "Although this paper does not cite Magnus Hestenes, it
is sometimes referenced in connection with the work in
\cite{Hestenes:1951:MGC, Hestenes:1951:S,
Rosser:1951:SCE, Hestenes:1952:MCG}.",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Ben-Israel:1964:DSD,
author = "Adi Ben-Israel",
title = "On direct sum decompositions of {Hestenes} algebras",
journal = j-ISRAEL-J-MATH,
volume = "2",
pages = "50--54",
month = mar,
year = "1964",
CODEN = "ISJMAP",
DOI = "https://doi.org/10.1007/BF02759734",
ISSN = "0021-2172 (print), 1565-8511 (electronic)",
ISSN-L = "0021-2172",
MRclass = "46.50",
MRnumber = "171172",
MRreviewer = "M. R. Hestenes",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Israel Journal of Mathematics",
journal-URL = "http://link.springer.com/journal/11856",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Deal:1964:BRM,
author = "Roy B. Deal",
title = "Book Review: {{\booktitle{Modern Mathematics for the
Engineer}}, Edited by Edwin F. Beckenbach. New York,
McGraw-Hill, 1956. xxii + 514 pp.}",
journal = j-PI-MU-EPSILON-J,
volume = "4",
number = "1",
pages = "22--22",
month = "Fall",
year = "1964",
CODEN = "PMEJBR",
ISSN = "0031-952X",
ISSN-L = "0031-952X",
bibdate = "Tue Oct 24 14:21:47 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.jstor.org/stable/24339253",
acknowledgement = ack-nhfb,
fjournal = "Pi Mu Epsilon Journal",
journal-URL = "https://www.jstor.org/journal/pimuepsilonj",
subject-dates = "Derrick Henry Lehmer (23 February 1905--22 May 1991);
George Elmer Forsythe (8 January 1917--9 April 1972);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Dreyfus:1965:BRC,
author = "S. E. Dreyfus",
title = "Book Review: {{\booktitle{Computing methods in
optimization problems}}, A. V. Balakrishnan and Lucien
W. Neustadt}",
journal = j-QUART-APPL-MATH,
volume = "23",
number = "3",
pages = "264--264",
year = "1965",
CODEN = "QAMAAY",
ISSN = "0033-569X (print), 1552-4485 (electronic)",
ISSN-L = "0033-569X",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "http://www.jstor.org/stable/43635529",
fjournal = "Quarterly of Applied Mathematics",
journal-URL = "http://dl.acm.org/citation.cfm?id=J641;
http://www.ams.org/journals/qam",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
urldate = "2023-10-24",
}
@Article{Guinn:1965:PBS,
author = "T. Guinn",
title = "The Problem of Bounded Space Coordinates as a Problem
of {Hestenes}",
journal = j-J-SOC-IND-APPL-MATH-A-ON-CONTROL,
volume = "3",
number = "2",
pages = "181--190",
month = jan,
year = "1965",
CODEN = "JSMCAL",
DOI = "https://doi.org/10.1137/0303015",
ISSN = "0887-4603 (print), 2168-359X (electronic)",
ISSN-L = "0887-4603",
MRclass = "93.40 (49.00)",
MRnumber = "192938",
MRreviewer = "L. D. Berkovitz",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/siamjcontrol.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Control",
journal-URL = "http://epubs.siam.org/journal/sjcodc",
onlinedate = "January 1965",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Guinn:1965:WHV,
author = "T. Guinn",
title = "Weakened Hypotheses for the Variational Problem
Considered by {Hestenes}",
journal = j-J-SOC-IND-APPL-MATH-A-ON-CONTROL,
volume = "3",
number = "3",
pages = "418--423",
month = jan,
year = "1965",
CODEN = "JSMCAL",
DOI = "https://doi.org/10.1137/0303027",
ISSN = "0887-4603 (print), 2168-359X (electronic)",
ISSN-L = "0887-4603",
MRclass = "93.40 (49.00)",
MRnumber = "192939",
MRreviewer = "L. D. Berkovitz",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/siamjcontrol.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Control",
journal-URL = "http://epubs.siam.org/journal/sjcodc",
onlinedate = "January 1965",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Bukovices:1967:BRM,
author = "E. Bukovices",
title = "Book Report: {M. R. Hestenes, Calculus of Variations
and Optimal Control Theory}",
journal = j-COMPUTING,
volume = "2",
number = "4",
pages = "374--374",
month = dec,
year = "1967",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Wed Nov 15 17:04:26 2000",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/computing.bib",
acknowledgement = ack-ec,
fjournal = "Computing",
journal-URL = "http://link.springer.com/journal/607",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@PhdThesis{Stephenson:1968:JST,
author = "Robert Allan Stephenson",
title = "{Jacobson} Structure Theory for {Hestenes} Ternary
Rings",
type = "{Ph.D.} dissertation",
school = "University of California, Riverside",
address = "Riverside, CA, USA",
pages = "38 (est.)",
year = "1968",
MRclass = "99-05",
MRnumber = "2617511",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.proquest.com/docview/302333090",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Young:1968:RCV,
author = "L. C. Young",
title = "Reviews: {{\em Calculus of Variations and Optimal
Control Theory}}, by {Magnus F. Hestenes}",
journal = j-AMER-MATH-MONTHLY,
volume = "75",
number = "10",
pages = "1135--1135",
month = dec,
year = "1968",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2315780",
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;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Smiley:1969:IHT,
author = "M. F. Smiley",
title = "An introduction to {Hestenes} ternary rings",
journal = j-AMER-MATH-MONTHLY,
volume = "76",
number = "3",
pages = "245--248",
month = mar,
year = "1969",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.2307/2316362",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "16.10 (20.00)",
MRnumber = "240130",
MRreviewer = "J. D. Stein, Jr.",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "http://www.jstor.org/journals/00029890.htm;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/journals/00029890.html",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Tabak:1970:BCM,
author = "Daniel Tabak",
title = "{B70-6}: {{\booktitle{Computing Methods in
Optimization Problems --- 2}}, L. A. Zadeh, L. W.
Neustadt, and A. V. Balakrishnan, Eds. (Academic Press,
Inc., NY, 1969, 393 pp.)}",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-19",
number = "10",
pages = "986--986",
month = oct,
year = "1970",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/T-C.1970.222811",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Wed Jul 13 08:01:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671404",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Magnus Hestenes",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InProceedings{Reid:1971:MCG,
author = "John Ker Reid",
title = "On the Method of Conjugate Gradients for the Solution
of Large Sparse Systems of Linear Equation",
crossref = "Reid:1971:LSS",
pages = "231--254",
year = "1971",
MRclass = "65F10",
MRnumber = "341836",
MRreviewer = "R. P. Tewarson",
bibdate = "Fri Oct 27 15:45:52 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
remark = "This paper drew new attention to the method of
conjugate gradients \cite[p. 83]{OLeary:2001:MCG}.",
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Friedman:1973:RTM,
author = "Kenneth Friedman",
title = "Replies to {Tribus} and {Motroni} and to {Gage} and
{Hestenes}",
journal = j-J-STAT-PHYS,
volume = "9",
number = "3",
pages = "265--269",
month = nov,
year = "1973",
CODEN = "JSTPSB",
DOI = "https://doi.org/10.1007/BF01008732",
ISSN = "0022-4715 (print), 1572-9613 (electronic)",
ISSN-L = "0022-4715",
bibdate = "Thu Aug 28 18:23:00 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/jstatphys1970.bib",
URL = "http://link.springer.com/article/10.1007/BF01008732",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Physics",
journal-URL = "http://link.springer.com/journal/10955",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Rockafellar:1973:MMH,
author = "R. T. Rockafellar",
title = "The multiplier method of {Hestenes} and {Powell}
applied to convex programming",
journal = j-J-OPT-THEORY-APPL,
volume = "12",
number = "6",
pages = "555--562",
month = dec,
year = "1973",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00934777",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "90C30",
MRnumber = "334953",
MRreviewer = "E. G. Gol\cprime shte\u{\i}n",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Stephenson:1973:JST,
author = "Robert Allan Stephenson",
title = "{Jacobson} structure theory for {Hestenes} ternary
rings",
journal = j-TRANS-AM-MATH-SOC,
volume = "177",
pages = "91--98",
month = mar,
year = "1973",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.2307/1996585",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "16A78 (17E05)",
MRnumber = "335583",
MRreviewer = "William Lister",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Anonymous:1974:CAD,
author = "Anonymous",
title = "Collection of articles dedicated to {Magnus R.
Hestenes}",
journal = j-J-OPT-THEORY-APPL,
volume = "14",
number = "5",
pages = "445--584",
month = nov,
year = "1974",
CODEN = "JOTABN",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "00A10 (01A70)",
MRnumber = "342307",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
note = "{\bf 14} (1974), no. 5",
URL = "https://link.springer.com/journal/10957/volumes-and-issues/14-5",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Miele:1974:APM,
author = "A. Miele",
title = "An appreciation of {Professor M. R. Hestenes}",
journal = j-J-OPT-THEORY-APPL,
volume = "14",
number = "5",
pages = "445--451",
month = nov,
year = "1974",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00932841",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "01A70 (49-03 65-03)",
MRnumber = "342354",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
note = "Includes a list of 58 publications of Magnus
Hestenes.",
abstract = "This issue of the Journal of Optimization Theory and
Applications is dedicated to Professor Magnus R.
Hestenes, a leading scholar and a renowned researcher
in both pure mathematics and applied mathematics. On
the occasion of his retirement from the University of
California at Los Angeles, the Editors of JOTA honor
him for his pioneering work and his long lasting
influence on pure and applied mathematicians throughout
the world.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Fortin:1975:MSN,
author = "Michel Fortin",
title = "Minimization of some non-differentiable functionals by
the augmented {Lagrangian} method of {Hestenes} and
{Powell}",
journal = j-APPL-MATH-OPTIM,
volume = "2",
number = "3",
pages = "236--250",
month = sep,
year = "1975",
CODEN = "AMOMBN",
DOI = "https://doi.org/10.1007/BF01464269",
ISSN = "0095-4616 (print), 1432-0606 (electronic)",
ISSN-L = "0095-4616",
MRclass = "49D99",
MRnumber = "417897",
MRreviewer = "M. R. Hestenes",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Optimization",
journal-URL = "http://link.springer.com/journal/245",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Rupp:1975:CMM,
author = "R. D. Rupp",
title = "On the combination of the multiplier method of
{Hestenes} and {Powell} with {Newton}'s method",
journal = j-J-OPT-THEORY-APPL,
volume = "15",
number = "2",
pages = "167--187",
month = feb,
year = "1975",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/bf02665291",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "49D30 (65K05)",
MRnumber = "385677",
MRreviewer = "Gerard G. L. Meyer",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Spera:1975:RHR,
author = "Antonino Giorgio Spera",
title = "Radical of a {Hestenes} ring",
journal = "Atti Accad. Sci. Lett. Arti Palermo Parte I (4)",
volume = "35",
pages = "283--296",
year = "1975/76",
ISSN = "0365-0448",
MRclass = "17A40 (16A45)",
MRnumber = "538492",
MRreviewer = "I. M. H. Etherington",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Atti della Accademia di Scienze Lettere e Arti di
Palermo. Parte Prima. Scienze. Serie Quarta",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Stephanopoulos:1975:UHM,
author = "G. Stephanopoulos and A. W. Westerberg",
title = "The use of {Hestenes}' method of multipliers to
resolve dual gaps in engineering system optimization",
journal = j-J-OPT-THEORY-APPL,
volume = "15",
number = "3",
pages = "285--309",
month = mar,
year = "1975",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00933339",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "90C30 (49D30)",
MRnumber = "378833",
MRreviewer = "A. G{\"{o}}pfert",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Bartolozzi:1977:ATH,
author = "Federico Bartolozzi and Gianfranco Panella",
title = "Anelli ternari di {Hestenes} semplici, artiniani e
privi di ideali bilateri effettivi",
journal = j-RIC-MAT,
volume = "26",
number = "2",
pages = "255--275",
year = "1977",
CODEN = "RCMTAE",
ISSN = "0035-5038 (print), 1827-3491 (electronic)",
ISSN-L = "0035-5038",
MRclass = "16A78",
MRnumber = "466231",
MRreviewer = "J. R. Isbell",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Ricerche di Matematica",
journal-URL = "http://link.springer.com/journal/11587",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Cullum:1977:BRO,
author = "Jane Cullum",
title = "Book Review: {{\booktitle{Optimization Theory; The
Finite Dimensional Case}} (Magnus R. Hestenes)}",
journal = j-SIAM-REVIEW,
volume = "19",
number = "4",
pages = "750--752",
month = oct,
year = "1977",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1019126",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Sat Mar 29 09:52:46 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/19/4;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1977",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Jeroslow:1977:BRO,
author = "Robert G. Jeroslow",
title = "Book Review: {{\booktitle{Optimization theory, the
finite dimensional case}}, by Magnus R. Hestenes, John
Wiley and Sons, New York, London, Sydney, Toronto,
1975, xiii + 447}",
journal = j-BULL-AMS,
volume = "83",
number = "3",
pages = "324--336",
month = may,
year = "1977",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1090/s0002-9904-1977-14252-3",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Tue Oct 24 11:50:30 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Profera:1977:SAH,
author = "Luigi Profera",
title = "Simple {Artinian} {Hestenes} ternary rings",
journal = "Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat.
(8)",
volume = "62",
number = "3",
pages = "292--299",
year = "1977",
ISSN = "0392-7881",
MRclass = "08A05",
MRnumber = "497650",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Atti della Accademia Nazionale dei Lincei. Rendiconti.
Classe di Scienze Fisiche, Matematiche e Naturali.
Serie VIII",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Sciutti:1977:CCH,
author = "D. Sciutti",
title = "On a characterization of convergence for the
{Hestenes} method of multipliers",
journal = j-J-OPT-THEORY-APPL,
volume = "22",
number = "2",
pages = "227--237",
month = jun,
year = "1977",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00933164",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "65K05 (49D99)",
MRnumber = "451726",
MRreviewer = "Hwa-Shan Ho",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Spera:1978:HTR,
author = "Antonino Giorgio Spera",
title = "{Hestenes} ternary rings",
journal = "Rendiconti del Circolo Matematico di Palermo. Serie
II",
volume = "27",
number = "2",
pages = "289--304",
month = may,
year = "1978",
DOI = "https://doi.org/10.1007/BF02843940",
ISSN = "0009-725x (print), 1973-4409 (electronic)",
MRclass = "16A45 (17A40)",
MRnumber = "561180",
MRreviewer = "V. A. Artamonov",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Rend. Circ. Mat. Palermo (2)",
fjournal = "Rendiconti del Circolo Matematico di Palermo. Serie
II",
journal-URL = "https://link.springer.com/journal/12215",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Zuse:1979:REC,
author = "Konrad Zuse",
title = "{Die Rolle der ETH bei der Computerentwicklung. Dem
Andenken an Eduard Stiefel}. ({German}) [{The} role of
{ETH} in computer development: In memory of {Eduard
Stiefel}]",
journal = j-Z-ANGE-MATH-PHYS,
volume = "30",
number = "2",
pages = "399--403",
month = mar,
year = "1979",
CODEN = "ZAMPDB",
DOI = "https://doi.org/10.1007/bf01601951",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
bibdate = "Fri Oct 27 16:09:33 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib",
acknowledgement = ack-nhfb,
author-dates = "Konrad Zuse (22 June 1910--18 December 1995)",
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik
= Journal of Applied Mathematics and Physics}",
journal-URL = "http://link.springer.com/journal/33",
language = "German",
remark = "From \cite[p. 84]{OLeary:2001:MCG}: ``Stiefel was a
visionary who realized the enormous significance of the
new computing technology and the impact it would have
on mathematics and science. When he discovered in 1949
that a major computing engine, the Z4 of the German
designer Konrad Zuse, was sitting in the small alpine
village of Neukitchen, Germany, he traveled there and
arranged for the machine to be rented and moved to ETH.
Zuse, isolated by wartime secrecy, had independently
developed computing technology that in many ways was
superior to that available in the U.S. at the time
[13]. Stiefel's initiative made ETH the first European
university with an electronic computer, putting it in
the forefront of numerical computation and computer
science. This led to several breakthrough developments
by him and his colleagues, including the $ q d $
algorithm, the programming language ALGOL, and the
conjugate gradient algorithm.",
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolf Hestenes (13 February 1906--31 May
1991)",
}
@Article{Caggegi:1980:SHT,
author = "Andrea Caggegi",
title = "Simple {Hestenes} ternary rings, right {Artinian} and
with no effective two-sided ideals",
journal = "Rendiconti di Matematica. Serie VI.",
volume = "13",
number = "1",
pages = "85--103",
year = "1980",
ISSN = "0034-4427",
MRclass = "16A45 (17A40)",
MRnumber = "590735",
MRreviewer = "V. A. Artamonov",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Rend. Mat. (6)",
fjournal = "Rendiconti di Matematica. Serie VI",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Jittorntrum:1980:ACP,
author = "Krisorn Jittorntrum",
title = "Accelerated convergence for the {Powell--Hestenes}
multiplier method",
journal = j-MATH-PROG,
volume = "18",
number = "2",
pages = "197--214",
month = dec,
year = "1980",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01588314",
ISSN = "0025-5610 (print), 1436-4646 (electronic)",
ISSN-L = "0025-5610",
MRclass = "49D29 (65K10 90C30)",
MRnumber = "569001",
MRreviewer = "H. Mukai",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Bader:1981:QHT,
author = "Laura Bader and Anna Franchetta",
title = "Quasiprimitive {Hestenes} ternary rings",
journal = "Rendiconti di Matematica. Serie VII",
volume = "1",
number = "3",
pages = "411--430",
year = "1981",
ISSN = "0034-4427",
MRclass = "17A40 (51A25)",
MRnumber = "646029",
MRreviewer = "M. Stef\u{a}nescu",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Rend. Mat. (7)",
fjournal = "Rendiconti di Matematica. Serie VII. Universit\`a
degli Studi di Roma. Istituto Matematica Guido
Castelnuovo. Istituto di Matematica Applicata. Istituto
Nazionale di Alta Matematica",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Caggegi:1981:PHT,
author = "Andrea Caggegi",
title = "Primitive {Hestenes} ternary rings with minimal right
ideal",
journal = j-ANN-MAT-PURA-APPL-4,
volume = "128",
number = "1",
pages = "169--191",
month = dec,
year = "1981",
CODEN = "ANLMAE",
DOI = "https://doi.org/10.1007/BF01789472",
ISSN = "0003-4622",
MRclass = "17A40",
MRnumber = "640781",
MRreviewer = "M. Stef\u{a}nescu",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Annali di Matematica Pura ed Applicata. Serie Quarta",
journal-URL = "https://www.springer.com/journal/10231",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InProceedings{Snyman:1982:HST,
author = "J. A. Snyman",
booktitle = "Proceedings of the eighth {South} {African} symposium
on numerical mathematics ({Durban}, 1982)",
title = "A {Hestenes--Stiefel} type method for solving
nonlinear two-point boundary value problems",
publisher = "University of Natal",
address = "Durban, South Africa",
pages = "125--137",
year = "1982",
ISBN = "0-86980-316-6",
ISBN-13 = "978-0-86980-316-5",
MRclass = "34B15 (49B10)",
MRnumber = "749413",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Steihaug:1982:BRC,
author = "Trond Steihaug",
title = "Book Review: {{\booktitle{Conjugate Direction Methods
in Optimization}}, by Magnus Hestenes}",
journal = j-MATH-COMPUT,
volume = "38",
number = "157",
pages = "332--333",
month = jan,
year = "1982",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2007488",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 24 13:48:06 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.jstor.org/stable/2007488",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Hegedus:1987:GRHa,
author = "Csaba J. Heged{\H{u}}s",
title = "General recursions of {Hestenes--Stiefel} type for
conjugate directions. {I}. {The} direct recursion",
journal = "Alkalmazott Matematikai Lapok",
volume = "13",
number = "1--2",
pages = "83--96",
year = "1987/88",
ISSN = "0133-3399",
MRclass = "93B40 (49D07)",
MRnumber = "923189",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Alkalmaz. Mat. Lapok",
fjournal = "Alkalmazott Matematikai Lapok",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Hegedus:1987:GRHb,
author = "Cs. J. Heged{\H{u}}s",
title = "General recursions of {Hestenes--Stiefel} type for
conjugate directions. {II}. {The} reverse recursion",
journal = "Alkalmazott Matematikai Lapok",
volume = "13",
number = "3--4",
pages = "361--372",
year = "1987/88",
ISSN = "0133-3399",
MRclass = "65F99 (15A06 90C30)",
MRnumber = "978017",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Alkalmaz. Mat. Lapok",
fjournal = "Alkalmazott Matematikai Lapok",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InCollection{Hansen:1988:RNS,
author = "P. C. Hansen",
editor = "E. F. Deprettere",
booktitle = "Singular Value Decomposition and Signal Processing",
title = "Reducing the Number of Sweeps in {Hestenes} Method",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
year = "1988",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Golub:1989:SHC,
author = "Gene H. Golub and Dianne P. O'Leary",
title = "Some History of the Conjugate Gradient and {Lanczos}
Algorithms: 1948--1976",
journal = j-SIAM-REVIEW,
volume = "31",
number = "1",
pages = "50--102",
month = mar,
year = "1989",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1031003",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65-03 (00A15 01A60 65-00 65Fxx 90-03)",
MRnumber = "90b:65003",
bibdate = "Mon Jan 20 10:31:25 MST 1997",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Parallel/par.lin.alg.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib",
URL = "http://www.jstor.org/stable/2030847",
abstract = "The conjugate gradient and Lanczos algorithms for
solving linear systems of equations and eigenproblems
represent very important computational innovations of
the early 1950s. These methods came into wide use only
in the mid-1970s. Shortly thereafter, vector computers
and massive computer memories made it possible to use
these methods to solve problems which could not be
solved in any other way. Since that time, the
algorithms have been further refined and have become a
basic tool for solving a wide variety of problems on a
wide variety of computer architectures. The conjugate
gradient algorithm has also been extended to solve
nonlinear systems of equations and optimization
problems, and this has had tremendous impact on the
computation of unconstrained and constrained
optimization problems. This paper gives some of the
history of the conjugate gradient and Lanczos
algorithms and an annotated bibliography for the period
1948--1976.",
acknowledgement = ack-nhfb,
affiliation = "Stanford Univ",
affiliationaddress = "Stanford, CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "723; 921",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "Algorithms; Computer Programming--Algorithms;
Conjugate Gradient Algorithm; Lanczos Algorithm;
Mathematical Techniques; Optimization--Theory; Variable
Metric Algorithms",
mynote = "June 1987 Maryland TR-1859",
subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Linear systems (direct and
iterative methods) \\ G.1.3 Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra,
Eigenvalues \\ G.1.3 Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix
inversion",
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Anonymous:1991:DMR,
author = "Anonymous",
title = "Deaths: {Magnus R. Hestenes}",
journal = j-NAMS,
volume = "38",
number = "6",
pages = "657--657",
month = jul # "\slash " # aug,
year = "1991",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "01A70",
MRnumber = "1125306",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.ams.org/journals/notices/199107",
acknowledgement = ack-nhfb,
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Anonymous:1991:MH,
author = "Anonymous",
title = "{Magnus Hestenes}: 1906--1991",
journal = j-NAMS,
volume = "38",
number = "7",
pages = "792--792",
month = sep,
year = "1991",
CODEN = "AMNOAN",
ISSN = "0002-9920 (print), 1088-9477 (electronic)",
ISSN-L = "0002-9920",
MRclass = "01A70",
MRnumber = "1125306",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/nams1990.bib",
URL = "https://www.ams.org/journals/notices/199109",
acknowledgement = ack-nhfb,
ajournal = "Notices Amer. Math. Soc.",
fjournal = "Notices of the American Mathematical Society",
journal-URL = "http://www.ams.org/notices/",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Berkovitz:1991:OMR,
author = "Len Berkovitz and Tony Chan and Alfred Hayes and
Dianne O'Leary and Richard Tapia",
title = "Obituary. [{Magnus Rudolf Hestenes}]",
journal = j-SIAM-NEWS,
volume = "24",
number = "5",
pages = "??--??",
month = sep,
year = "1991",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Tue Oct 24 12:34:15 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "https://sinews.siam.org/",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Misc{Chan:1991:MH,
author = "Tony Chan",
title = "{Magnus Hestenes}",
howpublished = "Netlib Web site.",
day = "4",
month = jun,
year = "1991",
bibdate = "Tue Oct 24 12:20:31 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.netlib.org/na-digest-html/91/v91n24.html#2",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Pellegrini:1991:EHN,
author = "L. Pellegrini",
title = "An extension of the {Hestenes} necessary condition",
journal = j-J-OPT-THEORY-APPL,
volume = "69",
number = "2",
pages = "297--309",
month = may,
year = "1991",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00940645",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "49J52 (49K27 90C26 90C48)",
MRnumber = "1106356",
MRreviewer = "J{\"{o}}rg Thierfelder",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Berkovitz:1992:MMR,
author = "Leonard D. Berkovitz",
title = "In memory of {Magnus R. Hestenes}",
journal = j-J-OPT-THEORY-APPL,
volume = "73",
number = "2",
pages = "225--227",
month = may,
year = "1992",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/BF00940178",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "01A70",
MRnumber = "1163257",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
remark = "Contains a list of 23 selected Hestenes
publications.",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Guo:1995:GCH,
author = "Wen Ying Guo and Da Chuan Xu and Gui Cheng Shen",
title = "Global convergence of the {Hestenes--Stiefel}
conjugate gradient method",
journal = "Kexue Tongbao (Chinese)",
volume = "40",
number = "23",
pages = "2113--2117",
year = "1995",
ISSN = "0023-074X (print), 2095-9419 (electronic)",
ISSN-L = "0023-074X",
MRclass = "65K10",
MRnumber = "1396219",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Kexue Tongbao. Chinese Science Bulletin",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Misc{Lee:1995:CPM,
author = "J. A. N. Lee",
title = "Computer Pioneers: {Magnus R. Hestenes}",
howpublished = "IEEE Web site.",
year = "1995",
bibdate = "Tue Oct 24 12:28:39 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://history.computer.org/pioneers/hestenes.html",
acknowledgement = ack-nhfb,
remark = "From the article: ``Hestenes and Eduard Stiefel (of
Zurich) devised the [conjugate gradient] method
independently, but merged their ideas into a single
paper in 1952 [\cite{Hestenes:1952:MCG}]. It took
almost 20 years for computer technology to catch up
with Hestenes' ideas, making possible the storage and
solution through conjugate gradients of large sparse
linear systems for which elimination methods were
impractical.''",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Qi:1996:MHS,
author = "Hou Duo Qi and Ji Ye Han and Guang Hui Liu",
title = "The modified {Hestenes--Stiefel} conjugate gradient
method",
journal = "Chinese Annals of Mathematics. Series A. Shuxue
Niankan. A Ji",
volume = "17",
number = "3",
pages = "277--284",
year = "1996",
ISSN = "1000-8314",
MRclass = "90C30 (65K05)",
MRnumber = "1431378",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Chinese Ann. Math. Ser. A",
fjournal = "Chinese Annals of Mathematics. Series A. Shuxue
Niankan. A Ji",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Chernov:1997:HFD,
author = "A. V. Chernov and V. M. Chernov",
editor = "G. Sommer and J. J. Koenderink",
booktitle = "Algebraic Frames for the Perception-Action Cycle.
{AFPAC 1997}",
title = "On {Hestenes}' Formalization for Describing Linear
Image Transforms",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1315",
pages = "164--175",
year = "1997",
CODEN = "LNCSD9",
DOI = "https://doi.org/10.1007/BFb0017866",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Apr 28 08:51:33 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/lncs1997b.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InCollection{Ferrarotti:1998:GHLa,
author = "Massimo Ferrarotti and Leslie C. Wilson",
booktitle = "Geometry {Seminars}, 1996--1997 ({Italian})
({Bologna})",
title = "Generalized {Hestenes} lemma and extension of
functions",
publisher = "Universit{\`a} degli Studi di Bologna, Dipartimento di
Matematica",
address = "Bologna, Italy",
pages = "99--109",
year = "1998",
MRclass = "58C25",
MRnumber = "1635640",
MRreviewer = "Enrique Outerelo Dom{\'\i}nguez",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Ferrarotti:1998:GHLb,
author = "Massimo Ferrarotti and Leslie C. Wilson",
title = "Generalized {Hestenes}' lemma and extension of
functions",
journal = j-TRANS-AM-MATH-SOC,
volume = "350",
number = "5",
pages = "1957--1975",
month = may,
year = "1998",
CODEN = "TAMTAM",
DOI = "https://doi.org/10.1090/S0002-9947-98-01925-4",
ISSN = "0002-9947 (print), 1088-6850 (electronic)",
ISSN-L = "0002-9947",
MRclass = "58C25 (26B05 58C05)",
MRnumber = "1422896",
MRreviewer = "Wies\l aw Paw\l ucki",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Transactions of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/tran/",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Durazzi:1999:NSD,
author = "Carla Durazzi",
title = "Numerical solution of discrete quadratic optimal
control problems by {Hestenes}' method",
journal = "Rendiconti del Circolo Matematico di Palermo. Serie
II. Supplemento",
volume = "58",
pages = "133--154",
year = "1999",
ISSN = "1592-9531",
MRclass = "49M15 (49M37 90C20)",
MRnumber = "1712298",
MRreviewer = "Ion N. Chryssoverghi",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
note = "Proceedings of the Workshop ``Numerical Methods in
Optimization'' (Cortona, 1997)''.",
acknowledgement = ack-nhfb,
ajournal = "Rend. Circ. Mat. Palermo (2) Suppl.",
fjournal = "Rendiconti del Circolo Matematico di Palermo. Serie
II. Supplemento",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Misc{Anonymous:19xx:MRH,
author = "Anonymous",
title = "{Magnus Rudolph Hestenes}",
howpublished = "Memorial Web site.",
year = "19xx",
bibdate = "Tue Oct 24 12:15:43 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.findagrave.com/memorial/186188943/magnus-rudolph-hestenes",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Dongarra:2000:GEI,
author = "Jack Dongarra and Francis Sullivan",
title = "{Guest Editors}' Introduction: The Top 10 Algorithms",
journal = j-COMPUT-SCI-ENG,
volume = "2",
number = "1",
pages = "22--23",
month = jan # "\slash " # feb,
year = "2000",
CODEN = "CSENFA",
DOI = "https://doi.org/10.1109/MCISE.2000.814652",
ISSN = "1521-9615 (print), 1558-366X (electronic)",
ISSN-L = "1521-9615",
bibdate = "Fri Oct 13 14:31:09 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/bibnet/subjects/fastmultipole.bib;
https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
note = "See correspondence \cite{Makino:2000:LEF}.",
URL = "http://dlib.computer.org/cs/books/cs2000/pdf/c1022.pdf;
http://www.computer.org/cse/cs1999/c1022abs.htm",
abstract = "In putting together this issue of CiSE, we knew three
things: it would be difficult to list just 10
algorithms; it would be fun to assemble the authors and
read their papers; and, whatever we came up with in the
end, it would be controversial. We tried to assemble
the 10 algorithms with the greatest influence on the
development and practice of science and engineering in
the 20th century. Following is our list (in
chronological order): Metropolis Algorithm for Monte
Carlo; Simplex Method for Linear Programming; Krylov
Subspace Iteration Methods; The Decompositional
Approach to Matrix Computations; The Fortran Optimizing
Compiler; QR Algorithm for Computing Eigenvalues;
Quicksort Algorithm for Sorting; Fast Fourier
Transform; Integer Relation Detection; Fast Multipole
Method",
acknowledgement = ack-nhfb,
fjournal = "Computing in Science and Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InCollection{OLeary:2001:IMS,
author = "Dianne P. O'Leary",
title = "Iteration Method for the Solution of the Eigenvalue
Problem of Linear Differential and Integral Operators",
crossref = "Lide:2001:CEM",
pages = "77--80",
year = "2001",
bibdate = "Wed Oct 25 15:17:38 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/taussky-todd-olga.bib",
URL = "https://nvlpubs.nist.gov/nistpubs/sp958-lide/077-080.pdf",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991); Olga Taussky-Todd (30 August 1906--7 October
1995)",
}
@InCollection{OLeary:2001:MCG,
author = "Dianne P. O'Leary",
title = "Methods of Conjugate Gradients for Solving Linear
Systems",
crossref = "Lide:2001:CEM",
pages = "81--85",
year = "2001",
bibdate = "Wed Oct 25 15:19:12 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib",
URL = "https://nvlpubs.nist.gov/nistpubs/sp958-lide/077-080.pdf",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Shi:2001:MHS,
author = "Zhen Jun Shi",
title = "A modified {Hestenes--Stiefel} conjugate gradient
method and its global convergence",
journal = "Mathematica Numerica Sinica. Jisuan Shuxue",
volume = "23",
number = "4",
pages = "393--406",
year = "2001",
ISSN = "0254-7791",
MRclass = "90C52 (65K10)",
MRnumber = "1881814",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Numer. Sin.",
fjournal = "Mathematica Numerica Sinica. Jisuan Shuxue",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InCollection{Sugon:2002:HSA,
author = "Qurino M. Sugon and Daniel McNamara",
booktitle = "Applications of geometric algebra in computer science
and engineering ({Cambridge}, 2001)",
title = "A {Hestenes} spacetime algebra approach to light
polarization",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "297--306",
year = "2002",
ISBN = "0-8176-4267-6",
ISBN-13 = "978-0-8176-4267-9",
MRclass = "78A10 (15A66)",
MRnumber = "1912532",
MRreviewer = "Jonathan Bain",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Bonettini:2004:HMS,
author = "S. Bonettini and E. Galligani and V. Ruggiero",
title = "{Hestenes} method for symmetric indefinite systems in
interior-point method",
journal = j-REND-MAT-APPL-1981,
volume = "24",
number = "1",
pages = "185--199",
year = "2004",
CODEN = "RNMTAN",
ISSN = "1120-7183",
ISSN-L = "1120-7183",
MRclass = "90C51 (65K05 90C46)",
MRnumber = "2130147",
MRreviewer = "Gong Yun Zhao",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://doaj.org/toc/2532-3350",
acknowledgement = ack-nhfb,
fjournal = "Rendiconti di Matematica e delle sue Applicazioni.
Serie VII",
journal-URL = "https://www1.mat.uniroma1.it/ricerca/rendiconti/",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Bonettini:2005:INM,
author = "Silvia Bonettini and Emanuele Galligani and Valeria
Ruggiero",
title = "An inexact {Newton} method combined with {Hestenes}
multipliers' scheme for the solution of
{Karush--Kuhn--Tucker} systems",
journal = j-APPL-MATH-COMP,
volume = "168",
number = "1",
pages = "651--676",
day = "1",
month = sep,
year = "2005",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2004.09.018",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
MRclass = "90C30 (65H10 90C51 90C55)",
MRnumber = "2170857",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0096300304006307",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003/",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Dai:2005:MHS,
author = "Zhi Feng Dai and Lan Ping Chen",
title = "A mixed {Hestenes--Stiefel} {Dan--Yuan} conjugate
gradient method",
journal = "Mathematica Numerica Sinica. Jisuan Shuxue",
volume = "27",
number = "4",
pages = "429--436",
year = "2005",
ISSN = "0254-7791",
MRclass = "90C52 (90C30)",
MRnumber = "2199853",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Numer. Sin.",
fjournal = "Mathematica Numerica Sinica. Jisuan Shuxue",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Ferrarotti:2008:RGH,
author = "Massimo Ferrarotti and Leslie C. Wilson",
title = "Remarks on the generalized {Hestenes}'s lemma",
journal = j-ROCKY-MOUNTAIN-J-MATH,
volume = "38",
number = "2",
pages = "461--469",
month = apr,
year = "2008",
CODEN = "RMJMAE",
DOI = "https://doi.org/10.1216/RMJ-2008-38-2-461",
ISSN = "0035-7596 (print), 1945-3795 (electronic)",
ISSN-L = "0035-7596",
MRclass = "58C05 (26E10 32B20)",
MRnumber = "2401564",
MRreviewer = "Antonio D{\'\i}az-Cano",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "The Rocky Mountain Journal of Mathematics",
journal-URL = "http://projecteuclid.org/euclid.rmjm",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Du:2009:EPH,
author = "Xue-wu Du and Yu Li and Qian Li and Shuai Qin",
title = "Exactness properties of the {Hestenes--Powell}
augmented {Lagrangian} function for inequality
constrained optimization problems",
journal = "Gongcheng Shuxue Xuebao",
volume = "26",
number = "1",
pages = "138--146",
year = "2009",
ISSN = "1005-3085",
MRclass = "90C30",
MRnumber = "2542528",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Gongcheng Shuxue Xuebao. Chinese Journal of
Engineering Mathematics",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Zhang:2009:NVH,
author = "Li Zhang",
title = "New versions of the {Hestenes--Stiefel} nonlinear
conjugate gradient method based on the secant condition
for optimization",
journal = "Computational \& Applied Mathematics",
volume = "28",
number = "1",
pages = "111--133",
year = "2009",
DOI = "https://doi.org/10.1590/S0101-82052009000100006",
ISSN = "1807-0302 (print), 2238-3603 (electronic)",
ISSN-L = "1807-0302",
MRclass = "90C52 (65K10 90C30)",
MRnumber = "2495829",
MRreviewer = "Warren L. Hare",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Comput. Appl. Math.",
fjournal = "Computational \& Applied Mathematics",
journal-URL = "https://www.scielo.br/j/cam/",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Rivaie:2010:MHS,
author = "Mohd Rivaie and Mustafa Mamat and Ismail Mohd and
Muhammad Fauzi",
title = "Modified {Hestenes--Steifel} conjugate gradient
coefficient for unconstrained optimization",
journal = "Journal of Interdisciplinary Mathematics",
volume = "13",
number = "3",
pages = "241--251",
month = jun,
year = "2010",
DOI = "https://doi.org/10.1080/09720502.2010.10700698",
ISSN = "0972-0502",
ISSN-L = "0972-0502",
MRclass = "90C52 (90C26 90C30)",
MRnumber = "2721955",
MRreviewer = "Jonas Koko",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Interdiscip. Math.",
fjournal = "Journal of Interdisciplinary Mathematics",
journal-URL = "https://www.tandfonline.com/journals/tjim20",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Wei:2010:MHS,
author = "Zeng Xin Wei and Hai Dong Huang and Yan Rong Tao",
title = "A modified {Hestenes--Stiefel} conjugate gradient
method and its convergence",
journal = "Journal of Mathematical Research and Exposition",
volume = "30",
number = "2",
pages = "297--308",
year = "2010",
ISSN = "1000-341X",
MRclass = "90C52 (90C30)",
MRnumber = "2656619",
MRreviewer = "Lyudmila N. Polyakova",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Math. Res. Exposition",
fjournal = "Journal of Mathematical Research and Exposition",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Dai:2012:GCM,
author = "Zhifeng Dai and Fenghua Wen",
title = "Global convergence of a modified {Hestenes--Stiefel}
nonlinear conjugate gradient method with {Armijo} line
search",
journal = j-NUMER-ALGORITHMS,
volume = "59",
number = "1",
pages = "79--93",
month = jan,
year = "2012",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-011-9477-2",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "90C30 (65K10 90C52)",
MRnumber = "2886438",
MRreviewer = "Marco Gaviano",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=59&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=59&issue=1&spage=79",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Zhang:2012:NCP,
author = "Li Zhang and Youhua Zhou",
title = "A note on the convergence properties of the original
three-term {Hestenes--Stiefel} method",
journal = "Advanced Modeling and Optimization",
volume = "14",
number = "1",
pages = "159--163",
year = "2012",
ISSN = "1841-4311",
MRclass = "90C52 (65K10 90C30)",
MRnumber = "2897440",
MRreviewer = "Jonas Koko",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Adv. Model. Optim.",
fjournal = "Advanced Modeling and Optimization. The Electronic
International Journal",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Yuan:2013:MHS,
author = "Gonglin Yuan and Maojun Zhang",
title = "A modified {Hestenes--Stiefel} conjugate gradient
algorithm for large-scale optimization",
journal = j-NUMER-FUNCT-ANAL-OPTIM,
volume = "34",
number = "8",
pages = "914--937",
month = aug,
year = "2013",
CODEN = "NFAODL",
DOI = "https://doi.org/10.1080/01630563.2013.777350",
ISSN = "0163-0563 (print), 1532-2467 (electronic)",
ISSN-L = "0163-0563",
MRclass = "90C30 (90C06 90C52)",
MRnumber = "3175602",
MRreviewer = "Giovanni Fasano",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Functional Analysis and Optimization. An
International Journal",
journal-URL = "http://www.tandfonline.com/loi/lnfa20",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Zhou:2013:SCM,
author = "Weijun Zhou and Youhua Zhou",
title = "On the strong convergence of a modified
{Hestenes--Stiefel} method for nonconvex optimization",
journal = "Journal of Industrial and Management Optimization",
volume = "9",
number = "4",
pages = "893--899",
year = "2013",
DOI = "https://doi.org/10.3934/jimo.2013.9.893",
ISSN = "1547-5816 (print), 1553-166X (electronic)",
ISSN-L = "1547-5816",
MRclass = "90C26 (90C52)",
MRnumber = "3119092",
MRreviewer = "Magdalena Nockowska-Rosiak",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Ind. Manag. Optim.",
fjournal = "Journal of Industrial and Management Optimization",
journal-URL = "https://www.aimsciences.org/jimo",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InProceedings{Shapiee:2014:NMH,
author = "Norrlaili Shapiee and Mohd Rivaie and Mustafa Mamat
and Ismail Mohd",
booktitle = "{AIP} Conference Proceedings",
title = "A new modification of {Hestenes--Stiefel} method with
descent properties",
volume = "1602",
publisher = pub-AIP,
address = pub-AIP:adr,
pages = "520--526",
year = "2014",
DOI = "https://doi.org/10.1063/1.4882535",
bibdate = "Tue Oct 24 17:11:42 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InProceedings{Sugihara:2014:RSP,
author = "Tomomichi Sugihara",
booktitle = "2014 {IEEE\slash RSJ} International Conference on
Intelligent Robots and Systems",
title = "Robust solution of prioritized inverse kinematics
based on {Hestenes--Powell} multiplier method",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "510--515",
year = "2014",
DOI = "https://doi.org/10.1109/IROS.2014.6942607",
bibdate = "Fri Oct 27 11:25:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InProceedings{Wang:2014:FIH,
author = "Xinying Wang and Joseph Zambreno",
booktitle = "2014 {IEEE} International Parallel \& Distributed
Processing Symposium Workshops",
title = "An {FPGA} Implementation of the {Hestenes--Jacobi}
Algorithm for Singular Value Decomposition",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "220--227",
year = "2014",
DOI = "https://doi.org/10.1109/IPDPSW.2014.29",
bibdate = "Fri Oct 27 11:25:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Babaie-Kafaki:2015:HHS,
author = "Saman Babaie-Kafaki and Reza Ghanbari",
title = "A hybridization of the {Hestenes--Stiefel} and
{Dai--Yuan} conjugate gradient methods based on a
least-squares approach",
journal = j-OPTIM-METHODS-SOFTW,
volume = "30",
number = "4",
pages = "673--681",
month = oct,
year = "2015",
DOI = "https://doi.org/10.1080/10556788.2014.966825",
ISSN = "1026-7670 (print), 1055-6788 (electronic)",
ISSN-L = "1026-7670",
MRclass = "90C53 (65K05)",
MRnumber = "3375668",
MRreviewer = "Ch'{\^e}ng Sh{\^e}ng Chien",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Optimization Methods \& Software",
journal-URL = "http://www.tandfonline.com/loi/goms20",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Dong:2015:MHS,
author = "Xiao Liang Dong and Hong Wei Liu and Yu Bo He and Xi
Mei Yang",
title = "A modified {Hestenes--Stiefel} conjugate gradient
method with sufficient descent condition and conjugacy
condition",
journal = j-J-COMPUT-APPL-MATH,
volume = "281",
number = "??",
pages = "239--249",
month = jun,
year = "2015",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2014.11.058",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65K10 (65F10 90C53)",
MRnumber = "3310897",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042714005378",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Sai:2015:SHS,
author = "Nao Erzai Sai and Xiao Yun Wu",
title = "Spectral {Hestenes--Steifel} conjugate gradient method
and its global convergence",
journal = "Mathematics in Practice and Theory. Shuxue de Shijian
yu Renshi",
volume = "45",
number = "18",
pages = "261--270",
year = "2015",
ISSN = "1000-0984",
MRclass = "90C53",
MRnumber = "3445301",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Pract. Theory",
fjournal = "Mathematics in Practice and Theory. Shuxue de Shijian
yu Renshi",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Sun:2015:MHS,
author = "Min Sun and Jing Liu",
title = "A modified {Hestenes--Stiefel} projection method for
constrained nonlinear equations and its linear
convergence rate",
journal = "Journal of Applied Mathematics and Computing",
volume = "49",
number = "1--2",
pages = "145--156",
month = sep,
year = "2015",
DOI = "https://doi.org/10.1007/s12190-014-0829-7",
ISSN = "1598-5865 (print), 1865-2085 (electronic)",
ISSN-L = "1598-5865",
MRclass = "65K10 (90C52)",
MRnumber = "3393771",
MRreviewer = "Lkhamsuren Altangerel",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Appl. Math. Comput.",
fjournal = "Journal of Applied Mathematics and Computing",
journal-URL = "https://link.springer.com/journal/12190",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Salleh:2016:EMH,
author = "Zabidin Salleh and Ahmad Alhawarat",
title = "An efficient modification of the {Hestenes--Stiefel}
nonlinear conjugate gradient method with restart
property",
journal = j-J-INEQUAL-APPL,
pages = "Paper No. 110, 14",
month = apr,
year = "2016",
DOI = "https://doi.org/10.1186/s13660-016-1049-5",
ISSN = "1029-242X",
ISSN-L = "1025-5834",
MRclass = "90C53 (65K10 90C30)",
MRnumber = "3482774",
MRreviewer = "Ya Xiang Yuan",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Inequalities and Applications",
journal-URL = "http://journalofinequalitiesandapplications.springeropen.com/",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Yuan:2016:MHS,
author = "Gonglin Yuan and Zehong Meng and Yong Li",
title = "A modified {Hestenes} and {Stiefel} conjugate gradient
algorithm for large-scale nonsmooth minimizations and
nonlinear equations",
journal = j-J-OPT-THEORY-APPL,
volume = "168",
number = "1",
pages = "129--152",
month = jul,
year = "2016",
CODEN = "JOTABN",
DOI = "https://doi.org/10.1007/s10957-015-0781-1",
ISSN = "0022-3239 (print), 1573-2878 (electronic)",
ISSN-L = "0022-3239",
MRclass = "65K05 (90C25 90C53)",
MRnumber = "3448521",
MRreviewer = "Etienne de Klerk",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Optimization Theory and Applications",
journal-URL = "http://link.springer.com/journal/volumesAndIssues/10957",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Babaie-Kafaki:2017:EHS,
author = "S. Babaie-Kafaki and R. Ghanbari",
title = "Extensions of the {Hestenes--Stiefel} and
{Polak--Ribi{\`e}re--Polyak} conjugate gradient methods
with sufficient descent property",
journal = "Bulletin of the Iranian Mathematical Society",
volume = "43",
number = "7",
pages = "2437--2448",
year = "2017",
ISSN = "1017-060X",
ISSN-L = "1017-060X",
MRclass = "90C53 (65K10)",
MRnumber = "3885678",
MRreviewer = "Sne\v{z}ana Djordjevi{\'c}",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.springer.com/journal/41980",
acknowledgement = ack-nhfb,
ajournal = "Bull. Iranian Math. Soc.",
fjournal = "Bulletin of the Iranian Mathematical Society",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Dong:2017:MNH,
author = "Xiao-Liang Dong and Hong-Wei Liu and Xiang-Li Li and
Yu-Bo He and Ze-Xian Liu",
title = "A modified nonmonotone {Hestenes--Stiefel} type
conjugate gradient methods for large-scale
unconstrained problems",
journal = j-NUMER-FUNCT-ANAL-OPTIM,
volume = "38",
number = "1",
pages = "39--50",
month = sep,
year = "2017",
CODEN = "NFAODL",
DOI = "https://doi.org/10.1080/01630563.2016.1232730",
ISSN = "0163-0563 (print), 1532-2467 (electronic)",
ISSN-L = "0163-0563",
MRclass = "90C52 (90C06 90C26 90C53)",
MRnumber = "3590820",
MRreviewer = "Mehiddin Al-Baali",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Functional Analysis and Optimization. An
International Journal",
journal-URL = "http://www.tandfonline.com/loi/lnfa20",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Dong:2017:SNT,
author = "Xiao-Liang Dong and De-Ren Han and Reza Ghanbari and
Xiang-Li Li and Zhi-Feng Dai",
title = "Some new three-term {Hestenes--Stiefel} conjugate
gradient methods with affine combination",
journal = j-OPTIMIZATION,
volume = "66",
number = "5",
pages = "759--776",
month = feb,
year = "2017",
CODEN = "OPTZDQ",
DOI = "https://doi.org/10.1080/02331934.2017.1295242",
ISSN = "0233-1934, 0323-3898",
ISSN-L = "0233-1934",
MRclass = "90C52 (65K10)",
MRnumber = "3628550",
MRreviewer = "Zhongwen Chen",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Optimization. A Journal of Mathematical Programming
and Operations Research",
journal-URL = "http://www.tandfonline.com/loi/gopt20",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@MastersThesis{Raihen:2017:CRH,
author = "Nurul Md Raihen",
title = "Convergence Rates for {Hestenes' Gram--Schmidt}
Conjugate Direction Method without Derivatives in
Numerical Optimization",
type = "{Master}'s thesis",
school = "University of Toledo",
address = "Toledo, OH, USA",
pages = "x + 37",
month = aug,
year = "2017",
bibdate = "Fri Oct 27 09:30:53 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
URL = "https://www.proquest.com/pqdtglobal/docview/2166237834",
acknowledgement = ack-nhfb,
advisor = "Ivie Stein, Jr.",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Wang:2017:TNS,
author = "Guofang Wang and Rui Shan and Wei Huang and Wen Liu
and Jingyi Zhao",
title = "Two new spectral conjugate gradient algorithms based
on {Hestenes--Stiefel}",
journal = j-J-ALGORITHMS-COMPUT-TECHNOL,
volume = "11",
number = "4",
pages = "345--352",
month = aug,
year = "2017",
DOI = "https://doi.org/10.1177/1748301817725296",
ISSN = "1748-3018 (print), 1748-3026 (electronic)",
ISSN-L = "1748-3018",
MRclass = "65K10 (90C53)",
MRnumber = "3726197",
MRreviewer = "Yekini Shehu",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Algorithms \& Computational Technology",
journal-URL = "https://journals.sagepub.com/home/ACT",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Babaie-Kafaki:2018:LHH,
author = "Saman Babaie-Kafaki and Reza Ghanbari",
title = "A linear hybridization of the {Hestenes--Stiefel}
method and the memoryless {BFGS} technique",
journal = "Mediterranean Journal of Mathematics",
volume = "15",
number = "3",
pages = "Paper No. 86, 10",
month = apr,
year = "2018",
DOI = "https://doi.org/10.1007/s00009-018-1132-x",
ISSN = "1660-5446 (print), 1660-5454 (electronic)",
ISSN-L = "1660-5446",
MRclass = "90C53 (65F35 65K05)",
MRnumber = "3787799",
MRreviewer = "Wah June Leong",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Mediterr. J. Math.",
fjournal = "Mediterranean Journal of Mathematics",
journal-URL = "https://www.springer.com/journal/9",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Baluch:2018:NMT,
author = "Bakhtawar Baluch and Zabidin Salleh and Ahmad
Alhawarat",
title = "A new modified three-term {Hestenes--Stiefel}
conjugate gradient method with sufficient descent
property and its global convergence",
journal = "Journal of Optimization",
volume = "2018",
pages = "Art. ID 5057096, 13",
month = sep,
year = "2018",
DOI = "https://doi.org/10.1155/2018/5057096",
ISSN = "2314-6486 (print), 2356-752X (electronic)",
ISSN-L = "2314-6486",
MRclass = "90C53 (65K10 90C52)",
MRnumber = "3861853",
MRreviewer = "Anders Linn{\'e}r",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Optim.",
fjournal = "Journal of Optimization",
journal-URL = "https://www.hindawi.com/journals/jopti/",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InProceedings{Cuomo:2018:PIH,
author = "Salvatore Cuomo and Livia Marcellino and Guglielmo
Navarra",
booktitle = "2018 26th {Euromicro} International Conference on
Parallel, Distributed and Network-based Processing
{(PDP)}",
title = "A Parallel Implementation of the
{Hestenes--Jacobi}-One-Sides Method Using {GPU-CUDA}",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "722--725",
year = "2018",
DOI = "https://doi.org/10.1109/PDP2018.2018.00118",
bibdate = "Fri Oct 27 11:25:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InProceedings{Sun:2018:RCP,
author = "Zhongbo Sun and Yufeng Lian and Shuaishi Liu and
Yantao Tian",
booktitle = "2018 {IEEE 8th} Annual International Conference on
{CYBER} Technology in Automation, Control, and
Intelligent Systems {(CYBER)}",
title = "A Rapidly Convergent Projected {Hestenes--Stiefel}
Conjugate Gradient Algorithm for Optimal Robust
Controller of Bipedal Walking Robots",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1094--1099",
year = "2018",
DOI = "https://doi.org/10.1109/CYBER.2018.8688205",
bibdate = "Fri Oct 27 11:25:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib",
acknowledgement = ack-nhfb,
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Amini:2019:MHS,
author = "Keyvan Amini and Parvaneh Faramarzi and Nasrin
Pirfalah",
title = "A modified {Hestenes--Stiefel} conjugate gradient
method with an optimal property",
journal = j-OPTIM-METHODS-SOFTW,
volume = "34",
number = "4",
pages = "770--782",
month = apr,
year = "2019",
DOI = "https://doi.org/10.1080/10556788.2018.1457150",
ISSN = "1026-7670 (print), 1055-6788 (electronic)",
ISSN-L = "1026-7670",
MRclass = "65K05 (90C26 90C52)",
MRnumber = "3957081",
MRreviewer = "C. S. Lalitha",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Optimization Methods \& Software",
journal-URL = "http://www.tandfonline.com/loi/goms20",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Awwal:2019:PHS,
author = "Aliyu Muhammed Awwal and Poom Kumam and Auwal Bala
Abubakar and Adamu Wakili",
title = "A projection {Hestenes--Stiefel}-like method for
monotone nonlinear equations with convex constraints",
journal = "Thai Journal of Mathematics",
volume = "17",
pages = "181--200",
year = "2019",
ISSN = "1686-0209",
ISSN-L = "1686-0209",
MRclass = "65H10 (90C52)",
MRnumber = "3922012",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Thai J. Math.",
fjournal = "Thai Journal of Mathematics",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Dong:2019:EAT,
author = "Xiao-Liang Dong and Ze-Xian Liu and Hong-Wei Liu and
Xiang-Li Li",
title = "An efficient adaptive three-term extension of the
{Hestenes--Stiefel} conjugate gradient method",
journal = j-OPTIM-METHODS-SOFTW,
volume = "34",
number = "3",
pages = "546--559",
month = oct,
year = "2019",
DOI = "https://doi.org/10.1080/10556788.2017.1418870",
ISSN = "1026-7670 (print), 1055-6788 (electronic)",
ISSN-L = "1026-7670",
MRclass = "65K05 (90C53)",
MRnumber = "3937045",
MRreviewer = "Nicolas Gillis",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Optimization Methods \& Software",
journal-URL = "http://www.tandfonline.com/loi/goms20",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Awwal:2020:PHS,
author = "Aliyu Muhammed Awwal and Lin Wang and Poom Kumam and
Hassan Mohammad and Wiboonsak Watthayu",
title = "A projection {Hestenes--Stiefel} method with spectral
parameter for nonlinear monotone equations and signal
processing",
journal = "Mathematical \& Computational Applications",
volume = "25",
number = "2",
pages = "Paper No. 27, 29",
month = may,
year = "2020",
DOI = "https://doi.org/10.3390/mca25020027",
ISSN = "1300-686X",
ISSN-L = "1300-686X",
MRclass = "65H10 (90C53 94A12)",
MRnumber = "4128230",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "Math. Comput. Appl.",
fjournal = "Mathematical \& Computational Applications",
journal-URL = "https://www.mdpi.com/journal/mca",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Hu:2020:SMH,
author = "Wujie Hu and Jinzhao Wu and Gonglin Yuan",
title = "Some modified {Hestenes--Stiefel} conjugate gradient
algorithms with application in image restoration",
journal = j-APPL-NUM-MATH,
volume = "158",
number = "??",
pages = "360--376",
month = dec,
year = "2020",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/j.apnum.2020.08.009",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "94A08 (90C53)",
MRnumber = "4140574",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/applnummath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0168927420302440",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Abubakar:2021:NTT,
author = "Auwal Bala Abubakar and Kanikar Muangchoo and
Abdulkarim Hassan Ibrahim and Abubakar Bakoji Muhammad
and Lateef Olakunle Jolaoso and Kazeem Olalekan Aremu",
title = "A New Three-Term {Hestenes--Stiefel} Type Method for
Nonlinear Monotone Operator Equations and Image
Restoration",
journal = j-IEEE-ACCESS,
volume = "9",
pages = "18262--18277",
year = "2021",
DOI = "https://doi.org/10.1109/ACCESS.2021.3053141",
ISSN = "2169-3536",
ISSN-L = "2169-3536",
bibdate = "Fri Oct 27 11:25:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Access",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Faramarzi:2021:STT,
author = "Parvaneh Faramarzi and Keyvan Amini",
title = "A spectral three-term {Hestenes--Stiefel} conjugate
gradient method",
journal = "4OR",
volume = "19",
number = "1",
pages = "71--92",
month = feb,
year = "2021",
DOI = "https://doi.org/10.1007/s10288-020-00432-3",
ISSN = "1614-2411 (print), 1619-4500 (electronic)",
ISSN-L = "1614-2411",
MRclass = "90C53 (65K05 90C26)",
MRnumber = "4235292",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib",
acknowledgement = ack-nhfb,
fjournal = "4OR. A Quarterly Journal of Operations Research",
journal-URL = "https://www.springer.com/journal/10288",
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolf Hestenes (13 February 1906--31 May
1991)",
}
@InProceedings{Halil:2021:MHS,
author = "Isam H. Halil and Khalil K. Abbo and Hassan H.
Ebrahim",
booktitle = "2021 7th International Conference on Contemporary
Information Technology and Mathematics {(ICCITM)}",
title = "Modifications of {Hestenes} and {Stiefel} {CG} Method
for Solving Unconstrained Optimization Problems",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "274--278",
year = "2021",
DOI = "https://doi.org/10.1109/ICCITM53167.2021.9677756",
bibdate = "Fri Oct 27 11:25:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib",
acknowledgement = ack-nhfb,
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@InProceedings{Japri:2021:NMH,
author = "Nur Athira Japri and Srimazzura Basri and Mustafa
Mamat",
booktitle = "{AIP} Conference Proceedings: {SCIEMATHIC 2020}",
title = "New modification of the {Hestenes--Stiefel} with
strong {Wolfe} line search",
volume = "2355",
publisher = pub-AIP,
address = pub-AIP:adr,
year = "2021",
DOI = "https://doi.org/10.1063/5.0053211",
bibdate = "Tue Oct 24 17:11:42 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Narayanan:2021:LHD,
author = "Sindhu Narayanan and P. Kaelo",
title = "A linear hybridization of {Dai--Yuan} and
{Hestenes--Stiefel} conjugate gradient method for
unconstrained optimization",
journal = j-NUM-MATH-THEORY-METHODS-APPL,
volume = "14",
number = "2",
pages = "527--539",
month = jun,
year = "2021",
DOI = "https://doi.org/10.4208/nmtma.oa-2020-0056",
ISSN = "1004-8979 (print), 2079-7338 (electronic)",
ISSN-L = "1004-8979",
MRclass = "65K10 (90C26 90C53)",
MRnumber = "4208436",
MRreviewer = "Marius Durea",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Mathematics. Theory, Methods and
Applications",
journal-URL = "https://global-sci.org/nmtma.html",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Misc{Anonymous:2022:NDO,
author = "Anonymous",
title = "{NBS} Discovers One of the Century's Top 10
Algorithms: Date 1952",
howpublished = "NIST Web site",
day = "14",
month = mar,
year = "2022",
bibdate = "Wed Oct 25 15:01:43 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
note = "See \cite{Dongarra:2000:GEI}.",
URL = "https://www.nist.gov/mathematics-statistics/nbs-discovers-one-centurys-top-10-algorithms",
abstract = "In 1952 NBS researchers published an algorithm for
solving systems of linear equations which would only
come to prominence two decades later as a standard
method for solving very large sparse systems on
supercomputers. It's impact has been so great that in
1999 one magazine listed it as one of the Top 10
Algorithms of the Century.",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{HassanIbrahim:2022:DFT,
author = "Abdulkarim {Hassan Ibrahim} and Poom Kumam and Basim
A. Hassan and Auwal Bala Abubakar and Jamilu Abubakar",
title = "A derivative-free three-term {Hestenes--Stiefel} type
method for constrained nonlinear equations and image
restoration",
journal = j-INT-J-COMPUT-MATH,
volume = "99",
number = "5",
pages = "1041--1065",
month = jul,
year = "2022",
CODEN = "IJCMAT",
DOI = "https://doi.org/10.1080/00207160.2021.1946043",
ISSN = "0020-7160",
ISSN-L = "0020-7160",
MRclass = "65K10 (90C26 90C53)",
MRnumber = "4404895",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Computer Mathematics",
journal-URL = "http://www.tandfonline.com/loi/gcom20",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Li:2022:MTT,
author = "Dandan Li and Yuangfei Li and Songhua Wang",
title = "A modified three terms {Hestenes--Stiefel} conjugate
gradient projection algorithm and its application",
journal = "Journal of Jilin University. Science Edition. Jilin
Daxue Xuebao. Lixue Ban",
volume = "60",
number = "1",
pages = "64--72",
year = "2022",
DOI = "https://doi.org/10.13413/j.cnki.jdxblxb.2021173",
ISSN = "1671-5489",
MRclass = "65K10 (90C53)",
MRnumber = "4390341",
MRreviewer = "Min Sun",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Jilin Univ. Sci.",
fjournal = "Journal of Jilin University. Science Edition. Jilin
Daxue Xuebao. Lixue Ban",
journal-URL = "http://kns.cnki.net/KNavi/JournalDetail?pcode=CJFD&pykm=JLDX",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Khoshsimaye-Bargard:2023:DFS,
author = "Maryam Khoshsimaye-Bargard and Ali Ashrafi",
title = "A descent family of the spectral {Hestenes--Stiefel}
method by considering the quasi-{Newton} method",
journal = j-OPTIM-METHODS-SOFTW,
volume = "38",
number = "3",
pages = "495--509",
month = jan,
year = "2023",
DOI = "https://doi.org/10.1080/10556788.2022.2142585",
ISSN = "1026-7670 (print), 1055-6788 (electronic)",
ISSN-L = "1026-7670",
MRclass = "90C26 (65K10 90C53)",
MRnumber = "4609392",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
fjournal = "Optimization Methods \& Software",
journal-URL = "http://www.tandfonline.com/loi/goms20",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Khoshsimaye-Bargard:2023:FMT,
author = "Maryam Khoshsimaye-Bargard and Ali Ashrafi",
title = "A family of the modified three-term
{Hestenes--Stiefel} conjugate gradient method with
sufficient descent and conjugacy conditions",
journal = "Journal of Applied Mathematics and Computing",
volume = "69",
number = "3",
pages = "2331--2360",
month = jan,
year = "2023",
DOI = "https://doi.org/10.1007/s12190-023-01839-x",
ISSN = "1598-5865 (print), 1865-2085 (electronic)",
ISSN-L = "1598-5865",
MRclass = "90C53 (90C06 90C26)",
MRnumber = "4594411",
MRreviewer = "Zhongwen Chen",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Appl. Math. Comput.",
fjournal = "Journal of Applied Mathematics and Computing",
journal-URL = "https://link.springer.com/journal/12190",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Wang:2023:CST,
author = "Xiaoliang Wang",
title = "A class of spectral three-term descent
{Hestenes--Stiefel} conjugate gradient algorithms for
large-scale unconstrained optimization and image
restoration problems",
journal = j-APPL-NUM-MATH,
volume = "192",
number = "??",
pages = "41--56",
month = oct,
year = "2023",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/j.apnum.2023.05.024",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65K10 (94A12)",
MRnumber = "4601011",
bibdate = "Tue Oct 24 12:40:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/tex/bib/applnummath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0168927423001538",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Carson:2024:TUC,
author = "Erin Carson and J{\"o}rg Liesen and Zden{\v{e}}k
Strako{\v{s}}",
title = "Towards understanding {CG} and {GMRES} through
examples",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "692",
number = "??",
pages = "241--291",
day = "1",
month = jul,
year = "2024",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2024.04.003",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Apr 24 13:20:32 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/linala2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0024379524001381",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Book{Hestenes:1933:CCV,
author = "Magnus R. Hestenes",
booktitle = "Contributions to the Calculus of Variations
1931--1932",
title = "Contributions to the Calculus of Variations
1931--1932",
publisher = pub-U-CHICAGO,
address = pub-U-CHICAGO:adr,
pages = "vii + 523",
year = "1933",
MRclass = "49-06,00B15",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
ZMnumber = "0006.40401",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
ZBmath = "3009090",
}
@Proceedings{Paige:1953:SLE,
editor = "L. J. (Lowell J.) Paige and Olga Taussky",
booktitle = "Simultaneous Linear Equations and the Determination of
Eigenvalues[: proceedings of a symposium held {23--25
August 1951 at the Institute for Numerical Analysis,
Los Angeles, California}]",
title = "Simultaneous Linear Equations and the Determination of
Eigenvalues[: proceedings of a symposium held {23--25
August 1951 at the Institute for Numerical Analysis,
Los Angeles, California}]",
volume = "29",
publisher = pub-NBS,
address = pub-NBS:adr,
pages = "126",
year = "1953",
LCCN = "QA3 .U5 no. 29",
bibdate = "Sun Dec 18 15:23:29 GMT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/taussky-todd-olga.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
series = "Applied Mathematics Series",
acknowledgement = ack-nhfb,
author-dates = "George Elmer Forsythe (8 January 1917--9 April 1972);
John Todd (16 May 1911--21 June 2007); Magnus Rudolf
Hestenes (13 February 1906--31 May 1991); Olga
Taussky-Todd (30 August 1906--7 October 1995)",
remark = "Reprinted in 1958. This symposium was the inspiration
for the later Gatlinburg conferences in numerical
analysis.",
tableofcontents = "1. Tentative classification of methods and
bibliography on solving systems of linear equations /
George E. Forsythe \\
2. Simultaneous systems of equations / A. M. Ostrowski
\\
3. The geometry of some iterative methods of solving
linear systems / Alston S. Householder \\
4. Solutions of linear systems of equations on a relay
machine / Carl-Erik Fr{\"o}berg \\
5. Some special methods of relaxation technique /
Eduard Stiefel \\
6. Errors of matrix computations / Paul S. Dwyer \\
7. Rapidly converging iterative methods for solving
linear equations / J. Barkley Rosser \\
8. Some problems in aerodynamics and structural
engineering related to eigenvalues / R. A. Frazer \\
9. Inclusion theorems for eigenvalues / H. Wielandt \\
10. On general computation methods for eigenvalues and
eigenfunctions / Gaetano Fichera \\
11. Variational methods for the approximation and exact
computation of eigenvalues / Alexander Weinstein \\
12. Determination of eigenvalues and eigenvectors of
matrices / Magnus R. Hestenes \\
13. New results in the perturbation theory of
eigenvalue problems / F. Rellich \\
14. Bounds for characteristic roots of matrices /
Alfred Brauer \\
15. Matrix inversion and solution of simultaneous
linear algebraic equations with the IBM 604 electronic
calculating punch / George W. Petrie, III \\
16. Experiments on the inversion of a $16 \times 16$
matrix / John Todd \\
17. A method of computing eigenvalues and eigenvectors
suggested by classical results on symmetric matrices /
Wallace Givens \\
18. Computations relating to inverse matrices / Jack
Sherman \\
19. Results of recent experiments in the analysis of
periods carried out in the Istituto Nazionale per le
Applicazioni del Calcolo / Gaetano Fichera",
}
@Book{Beckenbach:1956:MME,
editor = "Edwin Ford Beckenbach",
booktitle = "Modern Mathematics for the Engineer: First Series",
title = "Modern Mathematics for the Engineer: First Series",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xxii + 514",
year = "1956",
MRclass = "00A06",
bibdate = "Tue Oct 24 14:09:24 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib",
series = "University of California Engineering Extension
Series",
ZMnumber = "0071.04603",
acknowledgement = ack-nhfb,
author-dates = "Derrick Henry Lehmer (23 February 1905--22 May 1991);
George Elmer Forsythe (8 January 1917--9 April 1972);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
tableofcontents = "Part 1: Mathematical Models \\
1. Linear and Nonlinear Oscillations / Solomon
Lefschetz \\
2. Equilibrium Analysis: The Stability Theory of
Poincare and Liapunov / Richard Bellman \\
3. Exterior Ballistics / John W. Green \\
4. Elements of the Calculus of Variations / Magnus R.
Hestenes \\
5. Hyperbolic Partial Differential Equations and
Applications / Richard Courant \\
6. Boundary-Value Problems in Elliptic Partial
Differential Equations / Menahem M. Schiffer \\
7. The Elastostatic Boundary-Value Problems / Ivan S.
Sokolnikoff \\
Part 2: Probabilistic Problems \\
8. The Theory of Prediction / Norbert Wiener \\
9. The Theory of Games/ Frederic Bohnenblust \\
10. Applied Mathematics in Operations Research /
Gilbert W. King \\
11. The Theory of Dynamic Programming / Richard Bellman
\\
12. Monte Carlo Methods / George W. Brown \\
Part 3: Computational Considerations \\
13. Matrices in Engineering / Louis A. Pipes \\
14. Functional Transformations for Engineering Design /
John L. Barnes \\
15. Conformal Mapping Methods / Edwin F. Beckenbach \\
16. Nonlinear Methods / Charles B. Morrey, Jr. \\
17. What are Relaxation Methods? / George E. Forsythe
\\
18. Methods of Steep Descent / Charles B. Tompkins \\
19. High-Speed Computing Devices and Their Applications
/ Derrick H. Lehmer",
ZBmath = "3118547",
}
@Book{Beckenbach:1962:MME,
editor = "Edwin Ford Beckenbach",
booktitle = "Modern Mathematics for the Engineer: Second Series",
title = "Modern Mathematics for the Engineer: Second Series",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "xviii + 456",
year = "1962",
LCCN = "QA401 .B4",
MRclass = "00A06 35-01 46-01 60-01 65-01 93-01",
bibdate = "Tue Oct 24 17:46:41 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib",
note = "With an introduction by Magnus R. Hestenes.",
ZMnumber = "0094.03003",
acknowledgement = ack-nhfb,
author-dates = "David M. Young, Jr. (October 20, 1923--December 21,
2008); Magnus Rudolph Hestenes (13 February 1906--31
May 1991); Stanis{\l}aw Marcin Ulam (13 April 1909--13
May 1984)",
remark = "Reprinted in \cite{Beckenbach:2013:MMEb}.",
tableofcontents = "From Delta functions to distributions / Arthur
Erd{\'e}lyi \\
Operational methods for separable differential
equations / Bernard Friedman \\
Integral transforms / John W. Miles \\
Semigroup methods in the theory of partial differential
equations / Ralph S. Phillips \\
Asymptotic formulas and series / J. Barkley Rosser \\
Chance processes and fluctuations / William Feller \\
Information theory / David Blackwell \\
The mathematical theory of control processes / Richard
Bellman \\
Formulating and solving linear programs / George B.
Dantzig \\
The mathematical theory of inventory processes / Samuel
Karlin \\
Monte Carlo calculations in problems of mathematical
physics / Stanislaw M. Ulam \\
Difference equations and functional equations in
transmission-line theory / Raymond Redheffer \\
Characteristic-value problems in hydrodynamic and
hydromagnetic theory / Subrahmanyan Chandrasekhar \\
Applications of the theory of partial differential
equations to problems of fluid mechanics / Paul R.
Garabedian \\
The numerical solution of elliptic and parabolic
partial differential equations / David Young \\
Circle, sphere, symmetrization, and some classical
physical problems / George P{\'o}lya",
ZBmath = "3153221",
}
@Proceedings{Zadeh:1969:CMO,
editor = "Lotfi A. Zadeh and Lucien W. Neustadt and A. V.
Balakrishnan",
booktitle = "{Computing Methods in Optimization Problems. Papers
presented at the 2nd International Conference on
Computing Methods in Optimization Problems, San Remo,
Italy, September 9--13, 1968}",
title = "{Computing Methods in Optimization Problems. Papers
presented at the 2nd International Conference on
Computing Methods in Optimization Problems, San Remo,
Italy, September 9--13, 1968}",
volume = "14",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "ix + 393",
year = "1969",
LCCN = "QA402.5 .I5 1968",
bibdate = "Tue Oct 24 13:56:06 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
z3950.loc.gov:7090/Voyager",
series = "Lecture Notes in Operations Research and Mathematical
Economics",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
meetingname = "International Conference on Computing Methods in
Optimization Problems (2nd: 1968: San Remo, Italy)",
remark = "Sponsored by the Society for Industrial and Applied
Mathematics (SIAM), with the cooperation of the
University of California and the University of Southern
California.",
subject = "Mathematical optimization; Numerical analysis",
}
@Book{Reid:1971:LSS,
editor = "John Ker Reid",
booktitle = "Large Sparse Sets of Linear Equations: Proceedings of
the {Oxford Conference of the Institute of Mathematics
and its Applications held at St. Catherine's College,
Oxford, 5--8 April 1970}",
title = "Large Sparse Sets of Linear Equations: Proceedings of
the {Oxford Conference of the Institute of Mathematics
and its Applications held at St. Catherine's College,
Oxford, 5--8 April 1970}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 284",
year = "1971",
ISBN = "0-12-586150-8 (hardcover)",
ISBN-13 = "978-0-12-586150-2 (hardcover)",
LCCN = "QA195 .L37 1971",
MRclass = "65FXX",
MRnumber = "331742",
bibdate = "Fri Oct 27 15:41:08 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Russell:1976:CVC,
editor = "David L. Russell",
booktitle = "Calculus of Variations and Control Theory.
{Proceedings of a Symposium conducted by the
Mathematics Research Center, University of Wisconsin,
Madison, Wisconsin, September 22--24, 1975. Dedicated
to Laurence Chisholm Young on the occasion of his 70th
birthday}",
title = "Calculus of Variations and Control Theory.
{Proceedings of a Symposium conducted by the
Mathematics Research Center, University of Wisconsin,
Madison, Wisconsin, September 22--24, 1975. Dedicated
to Laurence Chisholm Young on the occasion of his 70th
birthday}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
bookpages = "xvi + 409",
pages = "xvi + 409",
year = "1976",
ISBN = "0-12-604150-4",
ISBN-13 = "978-0-12-604150-7",
LCCN = "QA3 .U45 no. 36 QA315; QA402.3",
bibdate = "Tue Oct 24 17:37:42 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib",
note = "Publication number 36.",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
tableofcontents = "Dedication / ix \\
Foreword / x \\
Preface / xv \\
A Class of Nonlinear Variational Problems Arising from
Min-Max Filter Problems / Leonard D. Berkovitz / 1 \\
Derivate Containers, Inverse Functions, and
Controllability / Jack Warga / 13 \\
Linear Hereditary Control Systems / E. Bruce Lee / 47
\\
Catastrophes of Economic Equilibria / Lawrence Markus /
173 \\
The Geometry of Differential Equations on Banach Space
/ Dahlard L. Lukes / 93 \\
Existence Theorems for Pareto Problems of Optimization
/ Lamberto Cesari and M. B. Suryanarayana / 139 \\
Dual Problems of Lagrange for Arcs of Bounded Variation
/ R. Tyrrell Rockafellar / 155 \\
Some Recent Developments in the Theory and Computation
of Linear Control Problems / John L. Casti / 193 \\
Variational Inequalities and Optimal Stopping Time
Problems / A. Bensoussan / 219 \\
Linear Systems in Banach Spaces / Stefan Rolewicz / 245
\\
Necessary Conditions for a General Control Problem /
Frank H. Clarke / 257 \\
Mathematical Programming without Differentiability /
Hubert Halkin / 279 \\
On Quadratic Control Problems / Magnus R. Hestenes /
289 \\
The Time-Optimal Problem for Boundary Control of the
Heat Equation / H. O. Fattorini / 305 \\
Boundary Observation and Control for the Heat Equation
/ Thomas I. Seidman / 321 \\
The Stabilization of Linear Functional Differential
Equations / Richard Datko / 353 \\
Stability-Spaces and Frequency-Domain Conditions / V.
M. Popov / 371 \\
Transversality and Natural Boundary Conditions by
Equivalent Problems in Calculus of Variations / Donald
R. Snow / 391 \\
Index / 405",
}
@Proceedings{Crane:1987:HAC,
editor = "G. E. Crane",
booktitle = "{HSNC'87: ACM Conference on the History of Scientific
and Numeric Computation, conference proceedings: papers
presented at the Conference, Princeton, New Jersey, May
13-15, 1987}",
title = "{HSNC'87: ACM Conference on the History of Scientific
and Numeric Computation, conference proceedings: papers
presented at the Conference, Princeton, New Jersey, May
13-15, 1987}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "viii + 150",
month = oct,
year = "1987",
ISBN = "0-89791-229-2",
ISBN-13 = "978-0-89791-229-7",
LCCN = "QA76 .A25 1987",
bibdate = "Tue Nov 14 13:59:59 MST 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
http://portal.acm.org/proceedings/hsnc/;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/gear-c-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib",
acknowledgement = ack-nhfb,
author-dates = "David M. Young, Jr. (October 20, 1923--December 21,
2008); George Elmer Forsythe (8 January 1917--9 April
1972); John Todd (16 May 1911--21 June 2007); John W.
Tukey (16 June 1915--26 July 2000); Leslie Fox (30
September 1918--1 August 1992); Magnus Rudolph Hestenes
(13 February 1906--31 May 1991)",
remark = "Sponsored by the Allegheny Region of the Association
for Computing Machinery in cooperation with ACM SIGNUM
and the Society for Industrial and Applied
Mathematics.",
subject = "Electronic data processing; Congresses; Electronic
digital computers; Ordinateurs; Congr{\`e}s; Electronic
data processing.; Electronic digital computers.",
subject-dates = "George Elmer Forsythe (8 January 1917--9 April 1972);
James H. Wilkinson (27 September 1919--5 October 1986);
John W. Tukey (16 June 1915--26 July 2000)",
tableofcontents = "H. H. Goldstine / Keynote address --- Remembrance
of things past / https://doi.org/10.1145/41579.41580 /
1--16 \\
L. Fox / Early numerical analysis in the United Kingdom
/ https://doi.org/10.1145/41579.41581 / 21--39 \\
J. Todd / The prehistory and ancient history of
computation at the U.S. National Bureau of Standards /
https://doi.org/10.1145/41579.41582 / 47--51 \\
D. J. Wheeler / Programmed computing at the
Universities of Cambridge and Illinois in the early
fifties / https://doi.org/10.1145/41579.41583 / 53--58
\\
The development of methods of using computers for
calculations in the early fifties at Cambridge and
Illinois Universities. They are the recollections of a
participant. \\
J. R. Rice / Mathematical software and ACM Publications
/ https://doi.org/10.1145/41579.41584 / 59--62 \\
M. Gutknecht / The pioneer days of scientific computing
in Switzerland / https://doi.org/10.1145/41579.41585 /
63--69 \\
M. R. Hestenes / Conjugacy and gradients in variational
theory and analysis /
https://doi.org/10.1145/41579.41586 / 71--90 \\
C.-E. Fr{\"o}berg / {B I T} --- a child of the computer
/ https://doi.org/10.1145/41579.41587 / 91--93 \\
I. Babuska / Comments on postwar development of
computational mathematics in some countries of Eastern
Europe / https://doi.org/10.1145/41579.41588 / 95--96
\\
J. W. Cooley / How the FFT gained acceptance /
https://doi.org/10.1145/41579.41589 / 97--100 \\
C. W. Gear, R. Skeel / The development of ODE methods:
a symbiosis between hardware and numerical analysis /
https://doi.org/10.1145/41579.41590 / 105--115 \\
D. M. Young / An historical review of iterative methods
/ https://doi.org/10.1145/41579.41591 / 117--123 \\
T. Oden / Some historic comments on finite elements /
https://doi.org/10.1145/41579.41592 / 125--130 \\
B. N. Parlett / J. H. Wilkinson's work and influence on
matrix computations /
https://doi.org/10.1145/41579.41593 / 133--138 \\
J. Varah / The work of George Forsythe and his students
/ https://doi.org/10.1145/41579.41594 / 139--150",
}
@Book{Nash:1990:HSC,
editor = "Stephen G. Nash",
booktitle = "A History of Scientific Computing",
title = "A History of Scientific Computing",
publisher = pub-AW # " and " # pub-ACM,
address = pub-AW # " and " # pub-ACM:adr,
pages = "xix + 359",
year = "1990",
ISBN = "0-201-50814-1",
ISBN-13 = "978-0-201-50814-7",
LCCN = "QA76.17 .H59 1990",
bibdate = "Wed Dec 15 10:39:57 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/gear-c-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;;
https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
z3950.loc.gov:7090/Voyager",
series = "ACM Press history series",
acknowledgement = ack-nhfb,
author-dates = "Charles William ``Bill'' Gear (1 February 1935--15
March 2022); Garrett Birkhoff (19 January 1911--22
November 1996); Magnus Rudolph Hestenes (13 February
1906--31 May 1991)",
remark = "Based on papers presented at the Conference on the
History of Scientific and Numeric Computation, held in
Princeton, NJ, 1987. A few brief mentions of Alston
Householder are indexed in the book, with photographs
of him on pages xvi and 344.",
subject = "Electronic data processing; History; Science; Data
processing",
tableofcontents = "Remembrance of things past / Herman H. Goldstine /
5--16 \\
The contribution of J. H. Wilkinson to numerical
analysis / B. N. Parlett / 17--30 \\
The influence of George Forsythe and his students /
James Varah / 31--40 \\
Howard H. Aiken and the computer / I. Bernard Cohen /
41--52 \\
Particles in their self-consistent field: from
Hartree's differential analyzer to Cray machines /
Oscar Buneman / 57--62 \\
Fluid dynamics, reactor computations, and surface
representation / Garrett Birkhoff / 63--87 \\
The development of ODE methods: a symbiosis between
hardware and numerical analysis / C. W. Gear and R. D.
Skeel / 88--105 \\
A personal retrospection of reservoir simulation /
Donald W. Peaceman / 106--129 \\
How the FFT gained acceptance / James W. Cooley /
133--140 \\
Origins of the simplex method / George B. Dantzig /
141--151 \\
Historical comments on finite elements / J. Tinsley
Oden / 152--166 \\
Conjugacy and gradients / Magnus R. Hestenes / 167--179
\\
A historical review of iterative methods / David M.
Young / 180--194 \\
Shaping the evolution of numerical analysis in the
computer age: the SIAM thrust / I. Edward Block /
199--205 \\
Reminiscences on the University of Michigan summer
schools, the Gatlinburg Symposia, and Numerische
Mathematik / Richard S. Varga / 206--210 \\
The origin of mathematics of computation and some
personal recollections / Eugene Isaacson / 211--216 \\
Mathematical software and ACM publications / John R.
Rice / 217--227 \\
BIT --- a child of the computer / Carl-Erik Fr{\"o}berg
/ 228--233 \\
The Los Alamos experience, 1943--1954 / N. Metropolis /
237--250 \\
The prehistory and early history of computation at the
U.S. National Bureau of Standards / John Todd /
251--268 \\
Programmed computing at the Universities of Cambridge
and Illinois in the early fifties / David J. Wheeler /
269--279 \\
Early numerical analysis in the United Kingdom / L. Fox
/ 280--300 \\
The pioneer days of scientific computing in Switzerland
/ Martin H. Gutknecht / 301--313 \\
The development of computational mathematics in
Czechoslovakia and the USSR / I. Babuska / 314--328 \\
The contribution of Leningrad mathematicians to the
development of numerical linear algebra, 1950--1986 /
V. N. Kublanovskaya / 329--338",
}
@Book{Lide:2001:CEM,
editor = "D. R. Lide",
booktitle = "A Century of Excellence in Measurements, Standards,
and Technology: {A} Chronicle of Selected {NBS\slash
NIST} Publications, 1901--2000",
title = "A Century of Excellence in Measurements, Standards,
and Technology: {A} Chronicle of Selected {NBS\slash
NIST} Publications, 1901--2000",
volume = "958",
publisher = pub-NTIS,
address = pub-NTIS:adr,
pages = "ix + 386",
year = "2001",
bibdate = "Wed Oct 25 15:09:56 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/taussky-todd-olga.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "NIST Special Publication",
URL = "https://nvlpubs.nist.gov/nistpubs/sp958-lide/cntsp958old.htm",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
tableofcontents = "Introduction / David R. Lide / 002 \\
The Absolute Measurement of Inductance / A-M. Jeffrey,
N. B. Belecki, and J. F. Mayo-Wells / 005 \\
Determination of the Constants of Total Radiation From
a Black Body / Albert C. Parr / 007 \\
The Testing of Thermal Insulators / Robert R. Zarr /
010 \\
Precipitation Hardening of Metal Alloys / Sam Coriell /
014 \\
Construction and Operation of a Simple Homemade Radio
Receiving Outfit / Brian Belanger / 016 \\
Methods for Standardizing and Testing Precision Gage
Blocks / Ted Doiron / 019 \\
Recommended Minimum Requirements for Small Dwelling
Construction / Joel P. Zingeser / 022 \\
Visibility of Radiant Energy / Jonathan E. Hardis / 025
\\
Test of the Severity of Building Fires / David Evans,
Daniel Gross, and Richard Wright / 028 \\
Calculation of Compounds in Portland Cements / Geoffrey
Frohnsdorff / 033 \\
Development of the Visual-Type Airway Radio-Beacon
System / Hans J. Oser / 038 \\
A Hydrogen Isotope of Mass 2 / Walter J. Hamer and H.
Steffen Peiser / 043 \\
Air Flow and Turbulence in Boundary Layers / Norman A.
Mease and James E. Potzick / 046 \\
Thermodynamic Properties of Water and Steam for Power
Generation / Allan H. Harvey and Johanna M. H. Levelt
Sengers / 049 \\
Absolute Pressure Calibrations of Microphones / Victor
Nedzelnitsky / 053 \\
Absolute Determination of the Ampere / E. R. Williams,
R. E. Elmquist, N. B. Belecki, and J. F. Mayo-Wells /
056 \\
Radio Proximity Fuzes / John W. Lyons, E. A. Brown, and
B. Fonoroff / 059 \\
Stability of Double-Walled Manganin Resistors / R.
Dziuba, N. B. Belecki, and J. F. Mayo-Wells / 063 \\
Manufacture of Paper for War Maps and Other
Applications / William K. Wilson / 066 \\
Transmission of Sound Waves in Gases at Low Pressures /
Thomas M. Proctor / 069 \\
Atomic Energy Levels and Other Spectroscopic Data /
Wolfgang L. Wiese / 073 \\
Iteration Method for the Solution of the Eigenvalue
Problem of Linear Differential and Integral Operators /
Dianne P. O'Leary / 077 \\
Methods of Conjugate Gradients for Solving Linear
Systems / Dianne P. O'Leary / 081 \\
Computer Development at the National Bureau of
Standards / Russell A. Kirsch / 086 \\
Thermal Converters as AC--DC Transfer Standards for
Current and Voltage Measurements at Audio Frequencies /
J. R. Kinard, Jr., N. B. Belecki, and J. F. Mayo-Wells
/ 090 \\
Selected Values of Chemical Thermodynamic Properties /
David R. Lide / 093 \\
Applied Inorganic Analysis / Charles M. Beck II / 097
\\
The Diamond Anvil Pressure Cell / Gasper Piermarini and
Stanley Block / 100 \\
Polymer Crystallization With Folded Chains / Freddy
Khoury, John Hoffman, and Tom Davis / 104 \\
Cryogenic Engineering / Richard H. Kropschot / 107 \\
Reversal of the Parity Conservation Law in Nuclear
Physics / Ralph P. Hudson / 111 \\
Effects of Configuration Interaction on Intensities and
Phase Shifts / Charles W. Clark / 116 \\
Electromagnetic Waves in Stratified Media / D. A. Hill
/ 120 \\
``Second Breakdown'' in Transistors / Harry A. Schafft
/ 123 \\
Stress Relaxation With Finite Strain / Elliot Kearsley
and Barry Bernstein / 126 \\
Realistic Evaluation of the Precision and Accuracy of
Instrument Calibration Systems / M. Carroll Croarkin /
129 \\
Experimental Statistics / M. Carroll Croarkin / 132 \\
Handbook of Mathematical Functions / Ronald F. Boisvert
and Daniel W. Lozier / 135 \\
Paths, Trees, and Flowers / Christoph Witzgall, Ronald
Boisvert, Geraldine Cheok, Saul Gass, Alan Goldman, and
James Lawrence / 140 \\
Concepts, Terminology, and Notation for Optical
Modulation / Calvin S. McCamy / 145 \\
Theory of Light Scattering in Fluids / Raymond D.
Mountain / 149 \\
Scaling Analysis of Thermodynamic Properties in the
Critical Region of Fluids / Raymond D. Mountain / 152
\\
Resonance Tunneling of Field Emitted Electrons Through
Adsorbates on Metal Surfaces / J. W. Gadzuk / 155 \\
Quantitative Electron Probe Microanalysis / Dale E.
Newbury / 160 \\
Limits for Qualitative Detection and Quantitative
Determination / Richard M. Lindstrom / 164 \\
Traceability: An Evolving Concept / Brian Belanger,
Stanley Rasberry, Ernest Garner, Carroll Brickencamp,
and Charles Ehrlich / 167 \\
Code for Information Interchange / Martha M. Gray / 172
\\
Consumer Information Series / Walter G. Leight and W.
Reeves Tilley / 174 \\
Theory of Isoperibol Calorimetry for Laser Power and
Energy Measurement / Thomas R. Scott / 178 \\
Influence of Water on Crack Growth in Glass / Edwin
Fuller, William Luecke, and Stephen Freiman / 181 \\
Phase Equilibria Diagrams / Ronald Munro, Howard
McMurdie, Helen Ondik, and Terrell Vanderah / 184 \\
Determination of Reduced Cells in Crystallography /
Alan D. Mighell, Vicky Lynn Karen, and Ronald Munro /
188 \\
Speed of Light From Direct Frequency and Wavelength
Measurements / Donald B. Sullivan / 191 \\
Connecting Visible Wavelength Standards With X Rays and
{gamma}Rays / Richard D. Deslattes / 194 \\
Laser Cooling of Atoms / D. B. Sullivan / 200 \\
Spin-Polarized Electrons / Daniel T. Pierce and Robert
J. Celotta / 203 \\
Needs for Radioactivity Standards and Measurements in
Different Fields / Bert Coursey / 209 \\
The Topografiner: An Instrument for Measuring Surface
Microtopography / J. S. Villarurubia, R. D. Young, F.
Scire, E. C. Teague, and J. W. Gadzuk / 214 \\
Electron-Stimulated Desorption / Ted Madey and John
Yates / 219 \\
Photochemistry of Small Molecules / James R. McNesby
and Ralph Klein / 224 \\
Role of Standard Reference Materials in Measurement
Systems / Thomas E. Gills / 227 \\
Metrology and Standardization to Assist Industrializing
Economies / Lewis M. Branscomb / 230 \\
Publications Taking Us Toward a Metric America / Ralph
A. Richter / 234 \\
A New Approach to Manipulator Control: The Cerebellar
Model Articulation Controller / James S. Albus / 237
\\
Three Dimensional Metrology / Ted Doiron / 241 \\
Initial Graphics Exchange Specifications / Sharon K.
Kemmerer / 246 \\
Data Encryption Standard / William E. Burr / 250 \\
OMNIDATA and the Computerization of Scientific Data /
John R. Rumble, Jr. / 254 \\
FORTRAN Test Programs / John Cugini / 258 \\
Design and Evaluation Criteria for Energy Conservation
in New Buildings / Jim L. Heldenbrand / 260 \\
Computer Program for Heating and Cooling Loads in
Buildings / George Walton / 266 \\
Methods for Testing and Rating the Performance of
Heating and Air Conditioning Systems / James E. Hill /
270 \\
System for Fire Safety Evaluation of Health Care
Facilities / Harold Nelson / 275 \\
Estimation of Rate of Heat Release by Means of Oxygen
Consumption Measurements / Kenneth D. Steckler / 280
\\
Probability-Based Load Criteria for Structural Design /
Bruce R. Ellingwood / 283 \\
Resistivity-Dopant Density Relationship for
Phosphorus-Doped Silicon / W. R. Thurber / 289 \\
Critical Data for Critical Needs / John R. Rumble, Jr.
/ 291 \\
Materials at Low Temperatures / Fred Fickett / 294 \\
Optical Fiber Characterization / D. L. Franzen / 297
\\
Quasicrystals / Ronald Munro, Frank Gale, and Carol
Handwerker / 300 \\
Protein Crystallography by Joint X-Ray and Neutron
Diffraction / Norman F. Berk / 303 \\
Strain Effects in Superconducting Compounds / J. W.
Ekin / 306 \\
Dental Research at the National Bureau of Standards /
John Tesk and Ronald Munro / 309 \\
Handbook for Standard Reference Materials Users /
Thomas E. Gills / 313 \\
A Practical Josephson Voltage Standard at One Volt / Y.
Tang, N. B. Belecki, and J. F. Mayo-Wells / 315 \\
Plane-Wave Scattering-Matrix Theory of Antennas and
Antenna-Antenna Interactions / A. G. Repjar and J. F.
Mayo-Wells / 319 \\
The Automated Manufacturing Research Facility / James
S. Albus / 322 \\
Submicrometer Linewidth Metrology / Michael T. Postek
and Robert D. Larrabee / 328 \\
Observation of Atoms Laser-Cooled Below the Doppler
Limit / Steven Rolston / 331 \\
Laser-Excited Hot-Electron Induced Desorption / J. W.
Gadzuk / 334 \\
Measurement of the Universal Gas Constant Using an
Acoustic Resonator / Michael R. Moldover / 339 \\
Thermal and Oxidative Degradation of Polymers / Takashi
Kashiwagi / 344 \\
HAZARD I: Software for Fire Hazard Assessment / Richard
Bukowski / 347 \\
Analysis of the Catastrophic Rupture of a Pressure
Vessel / Tom Siewert / 350 \\
Curing Those Uncontrollable Fits of Interaction / Don
Libes / 353 \\
Baldrige Criteria for Performance Excellence / Curt
Reimann and Debbie Smyth / 357 \\
The Advanced Technology Program / Robert Sienkiewicz
and Richard N. Spivack / 359 \\
NIST Manufacturing Extension Partnership / Anita
O'Brien / 363 \\
Questions and Answers on Quality / Maureen Breitenberg
/ 366 \\
Uniformity in Weights and Measures Laws and Regulations
/ Joan Koenig / 368 \\
Certification of 10 $\mu$m Diameter Polystyrene Spheres
(``Space Beads'') / Tom Lettieri / 371 \\
Bose--Einstein Condensation in a Dilute Atomic Vapor /
James Faller / 375 \\
Index / David R. Lide / 379",
}
@Book{Beckenbach:2013:MMEa,
editor = "Edwin Ford Beckenbach",
booktitle = "Modern Mathematics for the Engineer: First Series",
title = "Modern Mathematics for the Engineer: First Series",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xx + 514",
year = "2013",
ISBN = "0-486-49746-1 (paperback), 0-486-31611-4 (e-book)",
ISBN-13 = "978-0-486-49746-4 (paperback), 978-0-486-31611-6
(e-book)",
LCCN = "QA401 .B4 2013",
bibdate = "Wed Oct 25 06:56:51 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib",
note = "With an introduction by Royal Weller. Reprint of
\cite{Beckenbach:1956:MME}.",
series = "Dover books on engineering",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
subject = "Math{\'e}matiques de l'ing{\'e}nieur.",
tableofcontents = "Linear and nonlinear oscillations / Solomon
Lefschetz \\
Equilibrium analysis: the stability theory and Liapunov
/ Richard Bellman \\
Exterior ballistics / John W. Green \\
Elements of the calculus of variations / Magnus R.
Hestenes \\
Hyperbolic partial differential equations and
applications / Richard Courant \\
Boundary-value problems in elliptic partial
differential equations / Menahem M. Schiffer \\
The elastostatic boundary-value problems / Ivan S.
Sokolnikoff \\
The theory of prediction / Norbert Wiener \\
The theory of games / H. Frederic Bohnenblust \\
Applied mathematics in operations research / Gilbert W.
King \\
The theory of dynamic programming / Richard Bellman \\
Monte carlo methods / George W. Brown \\
Matrices in engineering / Louis A. Pipes \\
Functional transformations for engineering design /
John L. Barnes \\
Conformal mapping methods / Edwin F. Beckenbach \\
Nonlinear methods / Charles B. Morrey, Jr. \\
What are relaxation methods? / George E. Forsythe \\
Methods of steep descent / Charles B. Tompkins \\
High-speed computing devices and their applications /
Derrick H. Lehmer",
}
@Book{Beckenbach:2013:MMEb,
editor = "Edwin Ford Beckenbach",
booktitle = "Modern Mathematics for the Engineer: Second Series",
title = "Modern Mathematics for the Engineer: Second Series",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xviii + 456",
year = "2013",
ISBN = "0-486-31612-2 (e-book), 0-486-49747-X (paperback),
1-306-32668-0 (e-book)",
ISBN-13 = "978-0-486-31612-3 (e-book), 978-0-486-49747-1
(paperback), 978-1-306-32668-1 (e-book)",
LCCN = "QA401 .B39 2013",
bibdate = "Wed Oct 25 06:35:00 MDT 2023",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib",
note = "With an introduction by Magnus R. Hestenes. Reprint of
\cite{Beckenbach:1962:MME}.",
acknowledgement = ack-nhfb,
author-dates = "David M. Young, Jr. (October 20, 1923--December 21,
2008); Magnus Rudolph Hestenes (13 February 1906--31
May 1991); Stanis{\l}aw Marcin Ulam (13 April 1909--13
May 1984)",
tableofcontents = "From Delta functions to distributions / Arthur
Erd{\'e}lyi \\
Operational methods for separable differential
equations / Bernard Friedman \\
Integral transforms / John W. Miles \\
Semigroup methods in the theory of partial differential
equations / Ralph S. Phillips \\
Asymptotic formulas and series / J. Barkley Rosser \\
Chance processes and fluctuations / William Feller \\
Information theory / David Blackwell \\
The mathematical theory of control processes / Richard
Bellman \\
Formulating and solving linear programs / George B.
Dantzig \\
The mathematical theory of inventory processes / Samuel
Karlin \\
Monte Carlo calculations in problems of mathematical
physics / Stanislaw M. Ulam \\
Difference equations and functional equations in
transmission-line theory / Raymond Redheffer \\
Characteristic-value problems in hydrodynamic and
hydromagnetic theory / Subrahmanyan Chandrasekhar \\
Applications of the theory of partial differential
equations to problems of fluid mechanics / Paul R.
Garabedian \\
The numerical solution of elliptic and parabolic
partial differential equations / David Young \\
Circle, sphere, symmetrization, and some classical
physical problems / George P{\'o}lya",
}
