Abstract
Over the last 20 years a large number of algorithms has been published to improve the speed and domain of convergence of continued fractions. In this survey we show that these algorithms are strongly related. Actually, they essentially boil down to two main principles.
We also prove some results on asymptotic expansions of tail values of limit periodic continued fractions.
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Dedicated to Luigi Gatteschi on his seventieth birthday
This research was partially supported by The Norwegian Research Council and by the HMC project ROLLS, under contract CHRX-CT93-0416.
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Lorentzen, L. Computation of limit periodic continued fractions. A survey. Numer Algor 10, 69–111 (1995). https://doi.org/10.1007/BF02198297
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DOI: https://doi.org/10.1007/BF02198297
Keywords
- Continued fractions
- convergence acceleration
- analytic continuation
- asymptotic expansions
- modified approximants