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Since there are several continued fraction algorithms, we ask ourselves which of them provides the best approximation of a real number. The representation of a real number by a continued fraction can be viewed as a source of information about the number. For this purpose we need the notion of entropy, a rigorous tool at the crossroads between probability, information theory, and dynamical systems.

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Comparing the Efficiency of Different Continued Fraction Algorithms

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  • 发表日期：

    2025年

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  • Gabriela Ileana Sebe,
  • Dan Lascu

摘要

Since there are several continued fraction algorithms, we ask ourselves which of them provides the best approximation of a real number. The representation of a real number by a continued fraction can be viewed as a source of information about the number. For this purpose we need the notion of entropy, a rigorous tool at the crossroads between probability, information theory, and dynamical systems.