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Continued Fraction Interpolation of Preserving Horizontal Asymptote

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  • Yushan Zhao
  • Kaiwen Wu
  • Jieqing Tan
  • Hassan Raza

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 & Hassan Raza, 2022. "Continued Fraction Interpolation of Preserving Horizontal Asymptote," Journal of Mathematics, Hindawi, vol. 2022, pages 1-11, June.
    • Handle: RePEc:hin:jjmath:5662542
    DOI: 10.1155/2022/5662542
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