On the Bivariate Vector-Valued Rational Interpolation and Recovery Problems
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,...
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| Language: | English |
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MDPI AG
2025-04-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/14/5/341 |
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| author | Lixia Xiao Peng Xia Shugong Zhang |
| author_facet | Lixia Xiao Peng Xia Shugong Zhang |
| author_sort | Lixia Xiao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5b8501a4af454555bd5b8d0dd05a2aad |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-5b8501a4af454555bd5b8d0dd05a2aad2025-08-20T02:33:39ZengMDPI AGAxioms2075-16802025-04-0114534110.3390/axioms14050341On the Bivariate Vector-Valued Rational Interpolation and Recovery ProblemsLixia Xiao0Peng Xia1Shugong Zhang2School of Mathematics, Jilin University, Changchun 130012, ChinaSchool of Mathematics and Statistics, Liaoning University, Shenyang 110000, ChinaSchool of Mathematics, Jilin University, Changchun 130012, ChinaThis 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.https://www.mdpi.com/2075-1680/14/5/341vector-valued rational interpolationvector-valued rational recoveryGröbner basis |
| spellingShingle | Lixia Xiao Peng Xia Shugong Zhang On the Bivariate Vector-Valued Rational Interpolation and Recovery Problems Axioms vector-valued rational interpolation vector-valued rational recovery Gröbner basis |
| title | On the Bivariate Vector-Valued Rational Interpolation and Recovery Problems |
| title_full | On the Bivariate Vector-Valued Rational Interpolation and Recovery Problems |
| title_fullStr | On the Bivariate Vector-Valued Rational Interpolation and Recovery Problems |
| title_full_unstemmed | On the Bivariate Vector-Valued Rational Interpolation and Recovery Problems |
| title_short | On the Bivariate Vector-Valued Rational Interpolation and Recovery Problems |
| title_sort | on the bivariate vector valued rational interpolation and recovery problems |
| topic | vector-valued rational interpolation vector-valued rational recovery Gröbner basis |
| url | https://www.mdpi.com/2075-1680/14/5/341 |
| work_keys_str_mv | AT lixiaxiao onthebivariatevectorvaluedrationalinterpolationandrecoveryproblems AT pengxia onthebivariatevectorvaluedrationalinterpolationandrecoveryproblems AT shugongzhang onthebivariatevectorvaluedrationalinterpolationandrecoveryproblems |