The quotientdifference algorithm and the Padé table: an alternative form and a general continued fraction
Author:
J. H. McCabe
Journal:
Math. Comp. 41 (1983), 183197
MSC:
Primary 30B70; Secondary 10A30, 10F20, 41A21
MathSciNet review:
701633
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Abstract: The quotientdifference algorithm is applied to a given power series in a modified way, and various continued fractions provided by the algorithm are described in terms of their relationships with the Padé table for the power series. In particular a general continued fraction whose convergents form any chosen combination of horizontal or vertical connected sequences of Padé approximants is introduced.
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D. Bussonnais, Tous les Algorithms de Calcul par Recurrence des Approximations de Padé d'une Serie. Construction des Fractions Continues Correspondantes, Conference on Padé Approximation, Lille, 1978.
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 G. A. Baker, Jr., "The Padé approximant method and some related generalizations," The Padé Approximant in Theoretical Physics (G. A. Baker,Jr. and J. L. Gammel, eds.), Academic Press, New York, 1970, pp. 139.
 [2]
 D. Bussonnais, Tous les Algorithms de Calcul par Recurrence des Approximations de Padé d'une Serie. Construction des Fractions Continues Correspondantes, Conference on Padé Approximation, Lille, 1978.
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 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. 1829. MR 0240950 (39:2295)
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 W. B. Gragg, "The Padé table and its relation to certain algorithms of numerical analysis," SIAM Rev., v. 14, 1972, pp. 162. MR 0305563 (46:4693)
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 A. Sri Ranga, The Strong Hamburger Moment Problem, Internal Report, University of St. Andrews, 1982.
 [11]
 A. N. Stokes, "A stable quotient difference algorithm," Math. Comp., v. 34, 1980, pp. 515519. MR 559199 (81i:65019)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198307016333
PII:
S 00255718(1983)07016333
Keywords:
Continued fractions,
Padé approximants
Article copyright:
© Copyright 1983 American Mathematical Society
