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Open AccessArticle

Bivariate Thiele-Like Rational Interpolation Continued Fractions with Parameters Based on Virtual Points

1
School of Artificial Intelligence and Big Data, Hefei University, Hefei 230601, China
2
Institute of Intelligent Machines, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031, China
3
University of Science and Technology of China, Hefei 230026, China
*
Authors to whom correspondence should be addressed.
Mathematics 2020, 8(1), 71; https://doi.org/10.3390/math8010071
Received: 24 December 2019 / Revised: 30 December 2019 / Accepted: 31 December 2019 / Published: 2 January 2020
(This article belongs to the Special Issue Computational Mathematics, Algorithms, and Data Processing)
The interpolation of Thiele-type continued fractions is thought of as the traditional rational interpolation and plays a significant role in numerical analysis and image interpolation. Different to the classical method, a novel type of bivariate Thiele-like rational interpolation continued fractions with parameters is proposed to efficiently address the interpolation problem. Firstly, the multiplicity of the points is adjusted strategically. Secondly, bivariate Thiele-like rational interpolation continued fractions with parameters is developed. We also discuss the interpolant algorithm, theorem, and dual interpolation of the proposed interpolation method. Many interpolation functions can be gained through adjusting the parameter, which is flexible and convenient. We also demonstrate that the novel interpolation function can deal with the interpolation problems that inverse differences do not exist or that there are unattainable points appearing in classical Thiele-type continued fractions interpolation. Through the selection of proper parameters, the value of the interpolation function can be changed at any point in the interpolant region under unaltered interpolant data. Numerical examples are given to show that the developed methods achieve state-of-the-art performance. View Full-Text
Keywords: Thiele-like rational interpolation continued fractions with parameters; unattainable point; inverse difference; virtual point Thiele-like rational interpolation continued fractions with parameters; unattainable point; inverse difference; virtual point
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MDPI and ACS Style

Zou, L.; Song, L.; Wang, X.; Chen, Y.; Zhang, C.; Tang, C. Bivariate Thiele-Like Rational Interpolation Continued Fractions with Parameters Based on Virtual Points. Mathematics 2020, 8, 71.

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