Continued Fraction Interpolation of Preserving Horizontal Asymptote

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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2022-01, Vol.2022 (1)
Main Authors: Zhao, Yushan, Wu, Kaiwen, Tan, Jieqing
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Approximation
Asymptotes
Experiments
Interpolation
Mathematics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/5662542