Continued Fraction Interpolation of Preserving Horizontal Asymptote

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.