Optimal one-sided approximants of circular arc
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918133726445568 |
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| author | Praprotnik, Ada Šadl Vavpetič, Aleš Žagar, Emil |
| author_facet | Praprotnik, Ada Šadl Vavpetič, Aleš Žagar, Emil |
| contents | The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants interpolating boundary points is assumed. However, the study of approximants, which additionally interpolate corresponding tangent directions and curvatures at the boundary of an arc, is also considered. Several low-degree polynomial approximants are studied in detail. When several solutions fulfilling the interpolation conditions exist, the optimal one is characterized, and a numerical algorithm for its construction is suggested. Theoretical results are demonstrated with several numerical examples and a comparison with general (i.e. non-one-sided) approximants are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09129 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal one-sided approximants of circular arc Praprotnik, Ada Šadl Vavpetič, Aleš Žagar, Emil Numerical Analysis 65D05, 65D07, 65D17 The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants interpolating boundary points is assumed. However, the study of approximants, which additionally interpolate corresponding tangent directions and curvatures at the boundary of an arc, is also considered. Several low-degree polynomial approximants are studied in detail. When several solutions fulfilling the interpolation conditions exist, the optimal one is characterized, and a numerical algorithm for its construction is suggested. Theoretical results are demonstrated with several numerical examples and a comparison with general (i.e. non-one-sided) approximants are provided. |
| title | Optimal one-sided approximants of circular arc |
| topic | Numerical Analysis 65D05, 65D07, 65D17 |
| url | https://arxiv.org/abs/2401.09129 |