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Convergence Acceleration of Some Continued Fractions

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Abstract

The tails of a continued fraction satisfy a bilinear recurrent equation. Transforming iteratively these tails (in a special manner) as well as these equations one may obtain finally, for a given fraction, a new, so-called diagonal continued fraction (DF) having the same value. For many important classes of continued fractions the DF has a calculable analytical form and converges qualitatively faster. Using the same method one may transform some hypergeometrical series directly into fast convergent DFs.

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Authors and Affiliations

  1. Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 1410, 50-950, Wrocław 2, Poland

    Stefan Paszkowski

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  1. Stefan Paszkowski
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Paszkowski, S. Convergence Acceleration of Some Continued Fractions. Numerical Algorithms 32, 193–247 (2003). https://doi.org/10.1023/A:1024054205751

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  • DOI: https://doi.org/10.1023/A:1024054205751

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