Arbor, Vol 189, No 764 (2013)
Alan Turing y los orígenes de la eliminación gaussiana moderna
https://doi.org/10.3989/arbor.2013.764n6007
Froilán M. Dopico
Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM and Departamento de Matemáticas, Universidad Carlos III de Madrid, España
Resumen
Palabras clave
Referencias
Aspray, W. and Burks, A. (eds.) (1987). Papers of John von Neumann on Computing and Computer Theory. Cambridge, MA: MIT Press.
Carpenter, B. E. and Doran, R. W. (eds.) (1986). A. M. Turing's ACE report of 1946 and other papers. Cambridge, MA: MIT Press.
Demmel, J. W. (1997). Applied Numerical Linear Algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). http://dx.doi.org/10.1137/1.9781611971446
Dieudonné, J. (1981). "Von Neumann, Johan (or John)". In: Dictionary of Scientific Biographies, Vol. 14, C. C. Gillispie, ed., New York: Charles Scribner's Sons, pp. 89-92.
Dongarra, J. and Sullivan, F. (2000). "The top 10 algorithms of the century". Compnt. Sci. Eng., 2, pp. 22-23. http://dx.doi.org/10.1109/MCISE.2000.814652
Dopico, F. M. and Molera, J. M. (2012). "Accurate solution of structured linear systems via rank-revealing decompositions". IMA J. Nnmer. Anal., 32 (3), pp. 1096-1116. http://dx.doi.org/10.1093/imanum/drr023
Golub, G. and Van Loan, C. (1996). Matrix, Computations. Baltimore, MD: Johns Hopkins University Press, 3rd edition.
Grcar, J. F. (2011a). "How ordinary elimination became Gaussian elimination". Historia Math., 38 (2), pp. 163-218. http://dx.doi.org/10.1016/j.hm.2010.06.003
Grcar, J. F. (2011b). "John von Neumann's analysis of Gaussian elimination and the origins of modern Numerical Analysis". SIAM Rev., 53 (4), pp. 607-682. http://dx.doi.org/10.1137/080734716
Grcar, J. F. (2011c). "Mathematicians of Gaussian elimination". Notices Amer. Math. Soc., 58 (6), pp. 782-792.
Grigori, L.; Demmel, J. W. and Xiang, H. (2011). "CALU: a communication optimal LU factorization algorithm". SIAM J. Matrix, Anal. Appl., 32 (4), pp. 1317-1350. http://dx.doi.org/10.1137/100788926
Higham, N. J. (2002). Accuracy and Stability of Numerical Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), second edition. http://dx.doi.org/10.1137/1.9780898718027
Higham, N. J. (2011). "Gaussian elimination". Wiley Interdisciplinary Reviews: Computational Statistics, 3, pp. 230-238. http://dx.doi.org/10.1002/wics.164
Hodges, A. (2012). Alan Turing: the Enigma. Princeton, NJ: Princeton University Press, centenary edition.
Hotelling, H. (1943). "Some new methods in matrix calculation". Ann. Math. Statistics, 14, pp. 1-34. http://dx.doi.org/10.1214/aoms/1177731489
Rigal, J.-L. and Gaches, J. (1967). "On the compatibility of a given solution with the data of a linear system". J. Assoc. Compnt. Mach., 14, pp. 543-548. http://dx.doi.org/10.1145/321406.321416
Rojas, R. and Hashagen, U. (eds.) (2000). The First Computers. History and Architectures. Cambridge, MA: MIT Press.
Trefethen, L. N. (2012). "The Smart Money's on Numerical Analysts". SIAM News, 45 (9), 1-5.
Trefethen, L. N. and David Bau III (1997). Numerical Linear Algebra. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM). http://dx.doi.org/10.1137/1.9780898719574
Turing, A. M. (1948). "Rounding-off errors in matrix processes". Quart. J. Mech. Appl. Math., 1, pp. 287-308. http://dx.doi.org/10.1093/qjmam/1.1.287
von Neumann, J. and Goldstine, H. H. (1947). "Numerical inverting of matrices of high order". Bull. Amer. Math. Soc., 53, pp. 1021-1099. http://dx.doi.org/10.1090/S0002-9904-1947-08909-6
Wilkinson, J. H. (1954). "Linear Algebra on the Pilot ACE". In Automatic Digital Computation, Her Majesty's Stationery Office, London.
Wilkinson, J. H. (1960). "Error analysis of floating-point computation". Numer. Math., 2, pp. 319-340. http://dx.doi.org/10.1007/BF01386233
Wilkinson, J. H. (1961). "Error analysis of direct methods of matrix inversion. I". J. Assoc. Comput. Mach., 8, pp. 281-330. http://dx.doi.org/10.1145/321075.321076
Wilkinson, J. H. (1963). Rounding Errors in Algebraic Processes. Englewood Cliffs, N.J.: Prentice-Hall Inc.
Wilkinson, J. H. (1965). The Algebraic Eigenvalue Problem. Oxford: Clarendon Press.
Wilkinson, J. H. (1971a). "Modern error analysis". SIAM Rev., 13, pp. 548-568. http://dx.doi.org/10.1137/1013095
Wilkinson, J. H. (1971b). "Some comments from a numerical analyst". J. Assoc. Comput. Mach., 18, pp. 137-147. http://dx.doi.org/10.1145/321637.321638
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