A stable quotient-difference algorithm

Author:
A. N. Stokes

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

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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 in single-precision arithmetic. There is no significant build-up of error.

**[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 & J. A. MURPHY, ``Continued fractions which correspond to power series expansions at two points,''*J. Inst. Math. Appl.*, v. 17, 1976, pp. 233-247. MR**0422628 (54:10614)****[4]**L. M. MILNE-THOMPSON,*The Calculus of Finite Differences*, Macmillan, London, 1951. MR**0043339 (13:245c)**

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DOI:
https://doi.org/10.1090/S0025-5718-1980-0559199-4

Article copyright:
© Copyright 1980
American Mathematical Society