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Continued Fraction Interpolation of Preserving Horizontal Asymptote

Author

Listed:
  • Yushan Zhao
  • Kaiwen Wu
  • Jieqing Tan

Abstract

The classical Thiele‐type continued fraction interpolation is an important method of rational interpolation. However, the rational interpolation based on the classical Thiele‐type continued fractions cannot maintain the horizontal asymptote when the interpolated function is of a horizontal asymptote. By means of the relationship between the leading coefficients of the numerator and the denominator and the reciprocal differences of the continued fraction interpolation, a novel algorithm for the continued fraction interpolation is constructed in an effort to preserve the horizontal asymptote while approximating the given function with a horizontal asymptote. The uniqueness of the interpolation problem is proved, an error estimation is given, and numerical examples are provided to verify the effectiveness of the presented algorithm.

Suggested Citation

  • Yushan Zhao & Kaiwen Wu & Jieqing Tan, 2022. "Continued Fraction Interpolation of Preserving Horizontal Asymptote," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:5662542
    DOI: 10.1155/2022/5662542
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    References listed on IDEAS

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    1. Jia-Bao Liu & Yan Bao & Wu-Ting Zheng & Sakander Hayat, 2021. "NETWORK COHERENCE ANALYSIS ON A FAMILY OF NESTED WEIGHTED n-POLYGON NETWORKS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-15, December.
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