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Keywords = vector-valued rational interpolation

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21 pages, 678 KB  
Article
On the Bivariate Vector-Valued Rational Interpolation and Recovery Problems
by Lixia Xiao, Peng Xia and Shugong Zhang
Axioms 2025, 14(5), 341; https://doi.org/10.3390/axioms14050341 - 29 Apr 2025
Viewed by 578
Abstract
This paper investigates bivariate vector-valued rational interpolation and recovery problems with common divisors in their denominators. By leveraging these shared divisors and employing a component-wise rational interpolation approach, we reduce the degree of the interpolation problem. Furthermore, a new algorithm for recovering bivariate [...] Read more.
This paper investigates bivariate vector-valued rational interpolation and recovery problems with common divisors in their denominators. By leveraging these shared divisors and employing a component-wise rational interpolation approach, we reduce the degree of the interpolation problem. Furthermore, a new algorithm for recovering bivariate vector-valued rational functions is proposed. Experimental results demonstrate that, compared to classical algorithms, our method achieves faster computation speed without compromising accuracy. This advantage is particularly evident in the recovery of bivariate vector-valued rational functions. Full article
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16 pages, 343 KB  
Article
On the Univariate Vector-Valued Rational Interpolation and Recovery Problems
by Lixia Xiao, Peng Xia and Shugong Zhang
Mathematics 2024, 12(18), 2896; https://doi.org/10.3390/math12182896 - 17 Sep 2024
Cited by 1 | Viewed by 1168
Abstract
In this paper, we consider a novel vector-valued rational interpolation algorithm and its application. Compared to the classic vector-valued rational interpolation algorithm, the proposed algorithm relaxes the constraint that the denominators of components of the interpolation function must be identical. Furthermore, this algorithm [...] Read more.
In this paper, we consider a novel vector-valued rational interpolation algorithm and its application. Compared to the classic vector-valued rational interpolation algorithm, the proposed algorithm relaxes the constraint that the denominators of components of the interpolation function must be identical. Furthermore, this algorithm can be applied to construct the vector-valued interpolation function component-wise, with the help of the common divisors among the denominators of components. Through experimental comparisons with the classic vector-valued rational interpolation algorithm, it is found that the proposed algorithm exhibits low construction cost, low degree of the interpolation function, and high approximation accuracy. Full article
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