參考資料
1.
J. Demmel, I. Dumitriu, and O. Holtz, Fast linear algebra is stable, Numer. Math., 108(1):59–91, 2007.
2.
J. C. Domingues, Lacroix
and the Calculus, Birkhäuser, Basel,
2008.
3.
M. H. Doolittle, Method employed in the solution of normal equations and in the
adjustment of a triangularization, in Report of the Superintendent of the Coast and Geodetic
Survey … Ending with June, 1878,
pages 115–120. Government Printing Office,Washington, DC, 1881.
4.
S. Duff and J. K. Reid,
The multifrontal solution of indefinite sparse symmetric linear systems, ACM Trans. Math. Software, 9(3):302–325, 1983.
5.
G. W. Dunnington, Carl
Friedrich Gauss: Titan of Science,
Math. Assoc. Amer.,Washington, DC, 2nd edition, 2004.
6.
P. S. Dwyer, A matrix presentation of least squares and correlation theory
with matrix justification of improved methods of solution, Ann. Math. Statist., 15(1): 82–89, 1944.
7.
------,
The square rootmethod and its use in correlation and regression, J. Amer. Statist. Assoc., 40:493–503, 1945.
8.
L. Euler, Anleitung zur
Algebra, Lund, 1771.
9.
G. E. Forsythe, Solving linear algebraic equations can be interesting, Bull. Amer. Math. Soc., 59(4):299–329, 1953.
10.
G. E. Forsythe and C. B. Moler,
Computer Solution of Linear
Algebraic Systems,
Prentice-Hall, Englewood Cliffs, New Jersey, 1967.
11.
K. A. Fox, Agricultural Economists in the Econometric Revolution, Oxford Economic Papers, New Series, 41 (1):53–70, 1989.
12.
L. Fox, An
Introduction to Numerical Linear Algebra, Clarendon Press, Oxford, 1964.
13.
R. A. Frazer, W. J. Duncan, and A. R. Collar, Elementary Matrices and Some Applications to Dynamics and Differential
Equations, Cambridge University Press, Cambridge,
1938.
14.
C. F. Gauss, Theoria
Motus Corporum Coelestium in Sectionibus Conicis Solum Ambientium, Perthes and Besser, Hamburg, 1809.
15.
------,
Disquisitio de elementis ellipticis Palladis, Commentationes Societatis Regiae Scientiarum Gottingensis recentiores:
Commentationes classis mathematicae, 1 (1808–1811):1–26, 1810.
16.
------,
Anwendung der Wahrscheinlichkeitsrechnung auf eine Aufgabe der practischen
Geometrie, Astronomische Nachrichten, 1(6):81–86, January 1822.
17.
------,
Supplementum theoriae combinationis observationum erroribus minimis obnoxiae, Commentationes Societatis Regiae
Scientiarum Gottingensis recentiores: Commentationes classis mathematicae, 6 (1823–1827): 57–98, 1826.
18.
J. F. Grcar, How ordinary elimination became Gaussian elimination, Historia Math. 38(2):163Ð218, 201a. doi: 10.1016/j.hm.2010.06.003.
19.
------,
John von Neumann’s Analysis of Gaussian elimination and the origins of modern
numerical analysis, SIAM
Rev., to appear, 2011b.
20.
------,
Mathematics turned inside out: The intensive faculty versus the extensive
faculty, Higher Education, 61(6), 2011c. doi:
10.1007/s10734-010-9358-y.
21.
J. Green and J. LaDuke,
Pioneering Women in American Mathematics:
The Pre-1940 Ph.D.’s,
Amer. Math. Soc., Providence, 2009.
22.
N. Guicciardini, Derek Thomas Whiteside (1932–2008), Historia Math., 36(1):4–9, 2008.
23.
R. Hart, The
Chinese Roots of Linear Algebra,
Johns Hopkins University Press, Baltimore, 2011.
24.
T. Hawkins, Cauchy and the spectral theory of matrices, Historia Math., 2:1–29, 1975.
25.
------,
Another look at Cayley and the theory of matrices, Archives Internationales d’Histoire des Sciences, 27 (100):82–112, 1977a.
26.
------,
Weierstrass and the theory of matrices, Arch. Hist. Exact Sci., 17(2):119–164, 1977b.
27.
------,
Frobenius and the symbolical algebra of matrices, Arch. Hist. Exact Sci., 62(1):23–57, 2008.
28.
T. L. Heath, Diophantus
of Alexandria, Cambridge University
Press, Cambridge, 2nd edition, 1910.
29.
A. Heeffer, From the second unknown to the symbolic equation, in A. Heeffer
and M. Van Dyck, editors, Philosophical
Aspects of Symbolic Reasoning in Early Modern Mathematics, pages 57–101, College Publications,
London, 2011.
30.
J. Høyrup, Lengths, Widths,
Surfaces: A Portrait of Old Babylonian Algebra and Its Kin, Springer-Verlag, New York, 2002.
31.
B. M. Irons, A frontal solution program for finite element analysis, Int. J. Numer. Methods Eng., 2(1):5–32, 1970.
32.
H. Jensen, An attempt at a systematic classification of some methods for
the solution of normal equations, Meddelelse 18, Geodætisk Institut,
Copenhagen, 1944.
33.
M. Thomas à Kempis Kloyda, Linear and Quadratic Equations 1550–1660, Edwards Brothers, Ann Arbor, 1938,
University of Michigan dissertation.
34.
D. E. Knuth, George Forsythe and the Development of Computer Science, Comm. ACM, 15(8):721–726, 1972.
35.
S. F. Lacroix, Elements
of Algebra (Tr. J. Farrar), University
Press, Cambridge, Massachusetts, 1818.
36.
------,
Elemens d’algèbre, Chez Courcier, Paris, 5th edition,
1804.
37.
J. Laderman, The square root method for solving simultaneous linear
equations, Math. Tables Aids Comp., 3 (21):13–16, 1948.
38.
J. L. Lagrange, Recherches sur laméthode demaximis et minimis, Miscellanea Taurinensia, 1, 1759. Reprinted in OEuvres de
Lagrange, (J.-A. Serret, editor), vol. 1, pages 1–16, Gauthier–Villars, Paris,
1867.
39.
A. M. Legendre, Nouvelle
méthodes pour la determination des orbites des comètes, Chez Didot, Paris, 1805.
40.
U. Libbrecht, Chinese
Mathematics in the Thirteenth Century, MIT Press, Cambridge, 1973.
41.
G. L. Macomber, The influence of the English and French writers of the
sixteenth, seventeenth, and eighteenth centuries on the teaching of algebra,
M.A. thesis, University of California, Berkeley, 1923.
42.
J.-C. Martzloff, A History
of Chinese Mathematics (Tr. S.
S. Wilson), Springer, Berlin, 1997.
43.
I. Newton, Universal
Arithmetick, Senex, Taylor
et al., London, 1720.
44.
J. Peletier du Mans, L’Algebre,
Lyon, 1554.
45.
K. Plofker, Mathematics
in India, Princeton Univ. Press, 2009.
46.
R. R¯ashid, Entre
arithmétique et algèbre: Recherches sur l’histoire des mathématiques arabes, Société d’Édition Les Belles Lettres,
Paris, 1984.
47.
J. G. Reinis, The
Portrait Medallions of David d’Angers, Polymath Press, New York, 1999.
48.
E. Robson, Mathematics
in Ancient Iraq: A Social History,
Princeton Univ. Press, 2008.
49.
M. Rolle, Traité
d’algèbre, E. Michallet, Paris, 1690.
50.
K. Shen, J. N. Crossley, and A. W.-C. Lun, The Nine Chapters of the Mathematical Art Companion and Commentary, Oxford Univ. Press, New York, 1999.
51.
T. Simpson, A Treatise
of Algebra, John Nourse, London, 2nd edition, 1755.
52.
S. M. Stigler, The
History of Statistics: The Measurement of Uncertainty before 1900, Harvard University Press, Cambridge,
1986.
53.
V. Strassen, Gaussian elimination is not optimal, Numer. Math., 13(4):354–356, 1969.
54.
O. Taussky and J. Todd,
Cholesky, Toeplitz and the triangular factorization of symmetric matrices, Numerical Algorithms, 41:197–202, 2006.
55.
H. R. Tolley and M. Ezekiel,
The Doolittle Method …, J.
Amer. Statist. Assoc.,
22(160):497–500, 1927.
56.
J. F. Traub, Numerical mathematics and computer science, Comm. ACM, 15(7):537–541, 1972.
57.
A. M. Turing, Rounding-off errors in matrix processes, Quart. J. Mech. Appl. Math., 1(3):287–308, 1948.
58.
J. von Neumann and H. H. Goldstine, Numerical inverting of matrices of high order, Bull. Amer. Math. Soc., 53(11):1021–1099, 1947.
59.
C. Whaley and J. Dongarra,
Automatically tuned linear algebra software, in Proc. 1998 ACM/IEEE SC98 Conference, pages 1–27, IEEE, 1998.
60.
D. T. Whiteside, editor, The
Mathematical Papers of Isaac Newton, 8 vols., Cambridge University Press, 1968–1982.
61.
J. H. Wilkinson, Some comments from a numerical analyst, J. ACM, 18(2):137–147, 1970.
62.
F. Woepcke, Extrait du
Fakhrî, Paris, 1853.