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Some Monte Carlo experiments in computing multiple integrals


Authors: P. Davis and P. Rabinowitz
Journal: Math. Comp. 10 (1956), 1-8
MSC: Primary 65.0X
DOI: https://doi.org/10.1090/S0025-5718-1956-0076451-6
MathSciNet review: 0076451
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  • [1] See, however: J. Todd, ``Experiments in the solution of differential equations by Monte Carlo methods,'' J. Wash. Acad. of Sciences, v. 44, 1954, p. 377-381; N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, & E. Teller, ``Equation of state calculations by fast computing machines,'' J. Chem. Phys., v. 21, 1953, p. 1087-1092; R. D. Richtmyer, ``The evaluation of definite integrals and a quasi-Monte Carlo method based on the properties of algebraic numbers,'' Los Alamos Rep. 13, Oct. 1951. MR 0067584 (16:752c)
  • [2] H. Kahn, ``Modification of the Monte Carlo method,'' Seminar on Scientific Computation, International Business Machines Corp., November 1949. MR 0044896 (13:495c)
  • [3] For more detail on these methods see: O. Taussky & J. Todd, ``The generation and testing of pseudo-random numbers on SEAC.'' To appear.
  • [4] Ibid.
  • [5] See, e.g., H. Kahn, loc. cit.
  • [6] See, e.g., G. Pólya & G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Dover Publications, Inc., New York, v. 1, 1945, p. 70-77. MR 0015435 (7:418e)
  • [7] Richtmyer, loc. cit.
  • [8] Arthur Sard, ``Best approximate integration formulas,'' Am. J. Math., v. 71, 1949, p. 80-91; S. M. Nikolskii, ``K voprosa ob otzenkakh priblizhenii kvadraturnimi formulami,'' Uspekhi Math. Nauk, v. 51, p. 165-177; Philip Davis, ``Errors of numerical approximation for analytic functions,'' J. Rat. Mech. and Anal., v. 2, 1953, p. 303-313. MR 0029283 (10:576a)

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DOI: https://doi.org/10.1090/S0025-5718-1956-0076451-6
Article copyright: © Copyright 1956 American Mathematical Society

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