• [1] John Todd, Experiments in the solution of differential equations by Monte Carlo methods, J. Washington Acad. Sci. 44 (1954), 377–381. MR 67584
• [2] Herman Kahn, Modification of the Monte Carlo method, Proceedings, Seminar on Scientific Computation, November, 1949, International Business Machines Corp., New York, N. Y., 1950, pp. 20–27. MR 0044896
• [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] G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Dover Publications, New York, N. Y., 1945 (German). MR 0015435
• [7] Richtmyer, loc. cit.
• [8] Arthur Sard, Best approximate integration formulas; best approximation formulas, Amer. J. Math. 71 (1949), 80–91. MR 29283, https://doi.org/10.2307/2372095

Bibliography

[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)