Abstract
A new method of convergence acceleration is proposed for continued fractions of Poincaré's type 1. Each step of the method (and not only the first one, as in the Hautot method [1]) is based on an asymptotic behaviour of continued fraction tails. A theorem is proved detailing properties of the method in six cases considered here. Results of numerical tests for all Hautot's examples confirm a good performance of the method.
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References
A. Hautot, Convergence acceleration of continued fractions of Poincaré's type, Appl. Numer. Math. 4 (1988) 309–322.
W.B. Jones and W.J. Thron, Continued fractions in numerical analysis, Appl. Numer. Math. 4 (1988) 143–230.
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Paszkowski, S. Convergence acceleration of continued fractions of Poincaré's type 1. Numer Algor 2, 155–170 (1992). https://doi.org/10.1007/BF02145383
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DOI: https://doi.org/10.1007/BF02145383