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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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  • W. E. Milne, The remainder in linear methods of approximation, J. Research Nat. Bur. Standards 43 (1949), 501–511. MR 0036279
  • Robert E. Greenwood, Numerical integration for linear sums of exponential functions, Ann. Math. Statistics 20 (1949), 608–611. MR 32216, DOI https://doi.org/10.1214/aoms/1177729955
  • 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.
  • F. J. Murray, Linear equation solvers, Quart. Appl. Math. 7 (1949), 263–274. MR 31329, DOI https://doi.org/10.1090/S0033-569X-1949-31329-0
  • 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. W. Feller, Probability Theory. New York, 1950, v. 1, p. 52. G. Birkhoff & S. MacLane, A Survey of Modern Algebra. New York, 1948, p. 424.

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Article copyright: © Copyright 1952 American Mathematical Society