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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Convergence acceleration for generalized continued fractions
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by Paul Levrie and Lisa Jacobsen PDF
Trans. Amer. Math. Soc. 305 (1988), 263-275 Request permission


The main result in this paper is the proof of convergence acceleration for a suitable modification (as defined by de Bruin and Jacobsen) in the case of an $n$-fraction for which the underlying recurrence relation is of Perron-Kreuser type. It is assumed that the characteristic equations for this recurrence relation have only simple roots with differing absolute values.
  • M. G. de Bruin, Convergence of generalized $C$-fractions, J. Approx. Theory 24 (1978), no. 3, 177–207. MR 516674, DOI 10.1016/0021-9045(78)90023-0
  • M. G. de Bruin and L. Jacobsen, The dominance concept for linear recurrence relations with applications to continued fractions, Nieuw Arch. Wisk. (4) 3 (1985), no. 3, 253–266. MR 834113
  • —, Modification of generalised continued fractions. I, Lecture Notes in Math., vol 1237 (J. Gilewicz, M. Pindor, W. Siemaszko, Eds.), Springer-Verlag, Berlin, 1987, pp. 161-176.
  • J. R. Cash, A note on the numerical solution of linear recurrence relations, Numer. Math. 34 (1980), no. 4, 371–386. MR 577404, DOI 10.1007/BF01403675
  • P. Van der Cruyssen, Linear difference equations and generalized continued fractions, Computing 22 (1979), no. 3, 269–278 (English, with German summary). MR 620219, DOI 10.1007/BF02243567
  • Lisa Jacobsen, Modified approximants for continued fractions, construction and applications, Norske Vid. Selsk. Skr., no. 3 (1983). P. Kreuser, Über das Verhalten der Integrale homogener linearer Differenzengleichungen im Unendlichen, Thesis (Tubingen), Borna-Leipzig, 1914.
  • Oskar Perron, Über Summengleichungen und Poincarésche Differenzengleichungen, Math. Ann. 84 (1921), no. 1-2, 1–15 (German). MR 1512016, DOI 10.1007/BF01458689
  • Oskar Perron, Über lineare Differenzengleichungen und eine Anwendung auf lineare Differentialgleichungen mit Polynomkoeffizienten, Math. Z 72 (1959/1960), 16–24 (German). MR 0110902, DOI 10.1007/BF01162933
  • Wolfgang J. Thron and Haakon Waadeland, Accelerating convergence of limit-periodic continued fractions $K({a_n}/1)$, Numer. Math. 34 (1980), 155-170.
  • W. J. Thron and Haakon Waadeland, Analytic continuation of functions defined by means of continued fractions, Math. Scand. 47 (1980), no. 1, 72–90. MR 600079, DOI 10.7146/math.scand.a-11875
  • W. J. Thron and Haakon Waadeland, Convergence questions for limit periodic continued fractions, Rocky Mountain J. Math. 11 (1981), no. 4, 641–657. MR 639449, DOI 10.1216/RMJ-1981-11-4-641
  • William B. Jones, W. J. Thron, and Haakon Waadeland (eds.), Analytic theory of continued fractions, Notas de Matemática [Mathematical Notes], vol. 20, Springer-Verlag, Berlin-New York, 1982. MR 690450, DOI 10.1016/0378-4754(82)90113-6
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 305 (1988), 263-275
  • MSC: Primary 65B05; Secondary 65Q05
  • DOI:
  • MathSciNet review: 920158