Algebraic Curve Interpolation for Intervals via Symbolic-Numeric Computation
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909249432453120 |
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| author | Dehbi, Lydia Yang, Zhengfeng Peng, Chao Xu, Yaochen Zeng, Zhenbing |
| author_facet | Dehbi, Lydia Yang, Zhengfeng Peng, Chao Xu, Yaochen Zeng, Zhenbing |
| contents | Algebraic curve interpolation is described by specifying the location of N points in the plane and constructing an algebraic curve of a function f that should pass through them. In this paper, we propose a novel approach to construct the algebraic curve that interpolates a set of data (points or neighborhoods). This approach aims to search the polynomial with the smallest degree interpolating the given data. Moreover, the paper also presents an efficient method to reconstruct the algebraic curve of integer coefficients with the smallest degree and the least monomials that interpolates the provided data. The problems are converted into optimization problems and are solved via Lagrange multipliers methods and symbolic computation. Various examples are presented to illustrate the proposed approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07095 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic Curve Interpolation for Intervals via Symbolic-Numeric Computation Dehbi, Lydia Yang, Zhengfeng Peng, Chao Xu, Yaochen Zeng, Zhenbing General Mathematics Algebraic curve interpolation is described by specifying the location of N points in the plane and constructing an algebraic curve of a function f that should pass through them. In this paper, we propose a novel approach to construct the algebraic curve that interpolates a set of data (points or neighborhoods). This approach aims to search the polynomial with the smallest degree interpolating the given data. Moreover, the paper also presents an efficient method to reconstruct the algebraic curve of integer coefficients with the smallest degree and the least monomials that interpolates the provided data. The problems are converted into optimization problems and are solved via Lagrange multipliers methods and symbolic computation. Various examples are presented to illustrate the proposed approaches. |
| title | Algebraic Curve Interpolation for Intervals via Symbolic-Numeric Computation |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2407.07095 |