A stable quotient-difference algorithm
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- by A. N. Stokes PDF
- Math. Comp. 34 (1980), 515-519 Request permission
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
- I. Gargantini and P. Henrici, A continued fraction algorithm for the computation of higher transcendental functions in the complex plane, Math. Comp. 21 (1967), 18–29. MR 240950, DOI 10.1090/S0025-5718-1967-0240950-1 P. HENRICI, “The quotient-difference algorithm,” in Mathematical Methods for Digital Computers, Vol. 2 (A. Ralston & H. S. Wilf, Eds.), Wiley, New York, 1967.
- 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 422628
- L. M. Milne-Thomson, The Calculus of Finite Differences, Macmillan & Co., Ltd., London, 1951. MR 0043339
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Math. Comp. 34 (1980), 515-519
- MSC: Primary 65D15; Secondary 41A21
- DOI: https://doi.org/10.1090/S0025-5718-1980-0559199-4
- MathSciNet review: 559199