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Mathematics of Computation

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A stable quotient-difference algorithm


Author: A. N. Stokes
Journal: Math. Comp. 34 (1980), 515-519
MSC: Primary 65D15; Secondary 41A21
MathSciNet review: 559199
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Abstract: This paper shows how the arithmetic of the quotient-difference algorithm can be performed using the forward and backward difference tables of each column. This removes the tendency of the algorithm to amplify errors. As an application, 70 continued fraction coefficients are calculated for the modified Bessel function $ {K_0}(z)$ in single-precision arithmetic. There is no significant build-up of error.


References [Enhancements On Off] (What's this?)

  • [1] I. GARGANTINI & P. HENRICI, ``A continued fraction algorithm for the computation of higher transcendental functions in the complex plane,'' Math. Comp., v. 21, 1967, pp. 18-29. MR 0240950 (39:2295)
  • [2] P. HENRICI, ``The quotient-difference algorithm,'' in Mathematical Methods for Digital Computers, Vol. 2 (A. Ralston & H. S. Wilf, Eds.), Wiley, New York, 1967.
  • [3] J. H. McCabe and J. A. Murphy, Continued fractions which correspond to power series expansions at two points, J. Inst. Math. Appl. 17 (1976), no. 2, 233–247. MR 0422628
  • [4] L. M. Milne-Thomson, The Calculus of Finite Differences, Macmillan and Co., Ltd., London, 1951. MR 0043339

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1980-0559199-4
Article copyright: © Copyright 1980 American Mathematical Society