On the Univariate Vector-Valued Rational Interpolation and Recovery Problems
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 ident...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/18/2896 |
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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 | 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. |
| format | Article |
| id | doaj-art-912ade60ad06443cb9ebfdffcba53364 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-912ade60ad06443cb9ebfdffcba533642025-08-20T01:55:38ZengMDPI AGMathematics2227-73902024-09-011218289610.3390/math12182896On the Univariate 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, ChinaIn 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.https://www.mdpi.com/2227-7390/12/18/2896vector-valued rational interpolationvector-valued rational recoveryGröbner basis |
| spellingShingle | Lixia Xiao Peng Xia Shugong Zhang On the Univariate Vector-Valued Rational Interpolation and Recovery Problems Mathematics vector-valued rational interpolation vector-valued rational recovery Gröbner basis |
| title | On the Univariate Vector-Valued Rational Interpolation and Recovery Problems |
| title_full | On the Univariate Vector-Valued Rational Interpolation and Recovery Problems |
| title_fullStr | On the Univariate Vector-Valued Rational Interpolation and Recovery Problems |
| title_full_unstemmed | On the Univariate Vector-Valued Rational Interpolation and Recovery Problems |
| title_short | On the Univariate Vector-Valued Rational Interpolation and Recovery Problems |
| title_sort | on the univariate vector valued rational interpolation and recovery problems |
| topic | vector-valued rational interpolation vector-valued rational recovery Gröbner basis |
| url | https://www.mdpi.com/2227-7390/12/18/2896 |
| work_keys_str_mv | AT lixiaxiao ontheunivariatevectorvaluedrationalinterpolationandrecoveryproblems AT pengxia ontheunivariatevectorvaluedrationalinterpolationandrecoveryproblems AT shugongzhang ontheunivariatevectorvaluedrationalinterpolationandrecoveryproblems |