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Error analysis of Miller's recurrence algorithm


Author: F. W. J. Olver
Journal: Math. Comp. 18 (1964), 65-74
MSC: Primary 65.80
DOI: https://doi.org/10.1090/S0025-5718-1964-0169406-9
MathSciNet review: 0169406
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Abstract: Miller's algorithm is a device for computing the most rapidly decreasing solution of a second-order linear difference equation. In this paper strict upper bounds are given for the errors in the values yielded by the algorithm, and general conclusions are drawn concerning the accuracy of the process.


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  • [1] British Association For The Advancement Op Science, ``Bessel functions, Part II,'' Mathematical Tables, v. X, Cambridge University Press, 1952.
  • [2] C. W. Jones, ``A short table for the Bessel functions $ {I_{n + \tfrac{1}{2}}}(x)$, $ ({2}/{\pi }\;){{K}_{n+\tfrac{1}{2}}}(x)$,'' Royal Society Shorter Mathematical Tables, No. 1, Cambridge University Press, 1952. MR 0051573 (14:500d)
  • [3] L. Fox, ``A short table for Bessel functions of integer orders and large arguments,'' Royal Society Shorter Mathematical Tables, No. 3, Cambridge University Press, 1954. MR 0065245 (16:403a)
  • [4] F. J. Corbató, ``On the computation of auxiliary functions for two-center integrals by means of a high-speed computer,'' J. Chem. Phys., v. 24, 1956, p. 452-453.
  • [5] I. A. Stegun & M. Abramowitz, ``Generation of Bessel functions on high speed computers,'' MTAC, v. 11, 1957, p. 255-257. MR 0093939 (20:459)
  • [6] J. B. Randels & R. F. Reeves, ``Note on empirical bounds for generating Bessel functions,'' Comm. Assoc. Comput. Mach., v. 1, May 1958, p. 3-5.
  • [7] M. Goldstein & R. M. Thaler, ``Recurrence techniques for the calculation of Bessel functions,'' MTAC, v. 13, 1959, p. 102-108. MR 0105794 (21:4530)
  • [8] F. J. Corbató & J. L. Uretsky, ``Generation of spherical Bessel functions in digital computers,'' J. Assoc. Comput. Mach., v. 6, 1959, p. 366-375. MR 0105792 (21:4528)
  • [9] National Bureau Of Standards, ``Handbook of mathematical functions,'' Appl. Math. Ser. 55, Government Printing Office, Washington, D. C. (In press.) (Especially Section 9.12, Examples 1 and 7.)
  • [10] M. Abramowitz, Review of a paper by J. Kaye, MTAC, v. 10, 1956, p. 176-177.
  • [11] W. Gautschi, ``Recursive computation of the repeated integrals of the error function,'' Math. Comp., v. 15, 1961, p. 227-232. MR 0136074 (24:B2113)
  • [12] A. Rotenberg, ``The calculation of toroidal harmonics,'' Math. Comp. v. 14, 1960, p. 274-276. MR 0115264 (22:6066)
  • [13] C. W. Clenshaw, ``The numerical solution of linear differential equations in Chebyshev series,'' Proc. Cambridge Phil. Soc., v. 53, 1957, p. 134-149. MR 0082196 (18:516a)
  • [14] L. Fox, ``Chebyshev methods for ordinary differential equations,'' Computer J., v. 4, 1962, p. 318-331. MR 0136521 (24:B2554)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1964-0169406-9
Article copyright: © Copyright 1964 American Mathematical Society

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