On polynomial interpolation in the monomial basis
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912258786852864 |
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| author | Shen, Zewen Serkh, Kirill |
| author_facet | Shen, Zewen Serkh, Kirill |
| contents | In this paper, we show that the monomial basis is generally as good as a well-conditioned polynomial basis for interpolation, provided that the condition number of the Vandermonde matrix is smaller than the reciprocal of machine epsilon. This leads to a practical algorithm for piecewise polynomial interpolation over general regions in the complex plane using the monomial basis. Our analysis also yields a new upper bound for the condition number of an arbitrary Vandermonde matrix, which generalizes several previous results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_10519 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On polynomial interpolation in the monomial basis Shen, Zewen Serkh, Kirill Numerical Analysis In this paper, we show that the monomial basis is generally as good as a well-conditioned polynomial basis for interpolation, provided that the condition number of the Vandermonde matrix is smaller than the reciprocal of machine epsilon. This leads to a practical algorithm for piecewise polynomial interpolation over general regions in the complex plane using the monomial basis. Our analysis also yields a new upper bound for the condition number of an arbitrary Vandermonde matrix, which generalizes several previous results. |
| title | On polynomial interpolation in the monomial basis |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2212.10519 |