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Mathematics of Computation

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The use of exponential sums in step by step integration


Authors: P. Brock and F. J. Murray
Journal: Math. Comp. 6 (1952), 63-78
MSC: Primary 65.0X
DOI: https://doi.org/10.1090/S0025-5718-1952-0047403-3
MathSciNet review: 0047403
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  • [1] W. E. Milne, The remainder in linear methods of approximation, J. Research Nat. Bur. Standards 43 (1949), 501–511. MR 0036279
  • [2] Robert E. Greenwood, Numerical integration for linear sums of exponential functions, Ann. Math. Statistics 20 (1949), 608–611. MR 0032216
  • [3] P. Brock & F. J. Murray, ``Planning and error analysis for the numerical solution of a test system of differential equations on the IBM sequence calculator,'' Cyclone Report, Reeves Instrument Corp., New York 28. See also F. J. Murray, ``Planning and error considerations for the numerical solution of a system of differential equations on a sequence calculator,'' MTAC, v. 4, p. 133-144.
  • [4] F. J. Murray, Linear equation solvers, Quart. Appl. Math. 7 (1949), 263–274. MR 0031329, https://doi.org/10.1090/S0033-569X-1949-31329-0
  • [5] L. H. Thomas of the Watson Scientific Computing Laboratory indicated this formula for $ {A_n}$ to the authors. He also indicated that the $ {A_n}$ are equal in absolute value to the coefficients of the Adams-Bashforth method of step by step numerical integration.
  • [6] W. Feller, Probability Theory. New York, 1950, v. 1, p. 52.
  • [7] G. Birkhoff & S. MacLane, A Survey of Modern Algebra. New York, 1948, p. 424.

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DOI: https://doi.org/10.1090/S0025-5718-1952-0047403-3
Article copyright: © Copyright 1952 American Mathematical Society