Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Convergence acceleration for generalized continued fractions


Authors: Paul Levrie and Lisa Jacobsen
Journal: Trans. Amer. Math. Soc. 305 (1988), 263-275
MSC: Primary 65B05; Secondary 65Q05
MathSciNet review: 920158
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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.


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

  • [1] Marcel G. de Bruin, Convergence of generalized $ C$-fractions, J. Approx. Theory 24 (1978), 177-207. MR 516674 (81a:30004)
  • [2] Marcel G. de Bruin and Lisa Jacobsen, The dominance concept for linear recurrence relations with applications to continued fractions, Nieuw Arch. Wisk. (4) 3 (1985), 253-266. MR 834113 (87m:30007)
  • [3] -, 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.
  • [4] J. R. Cash, A note on the numerical solution of linear recurrence relations, Numer. Math. 34 (1980), 371-386. MR 577404 (81g:65174)
  • [5] P. Van der Cruyssen, Linear difference equations and generalized continued fractions, Computing 22 (1979), 269-287. MR 620219 (82e:65129)
  • [6] Lisa Jacobsen, Modified approximants for continued fractions, construction and applications, Norske Vid. Selsk. Skr., no. 3 (1983).
  • [7] P. Kreuser, Über das Verhalten der Integrale homogener linearer Differenzengleichungen im Unendlichen, Thesis (Tubingen), Borna-Leipzig, 1914.
  • [8] Oskar Perron, Über Summengleichungen und Poincarésche Differenzengleichungen, Math. Ann. 84 (1921), 1-15. MR 1512016
  • [9] -, Über lineare Differenzengleichungen und eine Anwendung auf lineare Differentialgleichungen mit Polynomkoeffizienten, Math. Z. 72 (1959), 16-24. MR 0110902 (22:1770)
  • [10] Wolfgang J. Thron and Haakon Waadeland, Accelerating convergence of limit-periodic continued fractions $ K({a_n}/1)$, Numer. Math. 34 (1980), 155-170.
  • [11] -, Analytic continuation of functions defined by means of continued fractions, Math. Scand. 47 (1980), 72-90. MR 600079 (82c:30004)
  • [12] -, Convergence questions for limit-periodic continued fractions, Rocky Mountain J. Math. 11 (1981), 641-657. MR 639449 (83e:40002)
  • [13] W. B. Jones, W. J. Thron and H. Waadeland, Eds., Analytic theory of continued fractions, Proceedings Loen, Norway 1981, Lecture Notes in Math., vol. 932, Springer-Verlag, Berlin, 1982. MR 690450 (84b:30002)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 65B05, 65Q05

Retrieve articles in all journals with MSC: 65B05, 65Q05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0920158-4
PII: S 0002-9947(1988)0920158-4
Article copyright: © Copyright 1988 American Mathematical Society