The Fekete problem in segmental polynomial interpolation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913264726704128 |
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| author | Bruno, Ludovico Bruni Erb, Wolfgang |
| author_facet | Bruno, Ludovico Bruni Erb, Wolfgang |
| contents | In this article, we study the Fekete problem in segmental and combined nodal-segmental univariate polynomial interpolation by investigating sets of segments, or segments combined with nodes, such that the Vandermonde determinant for the respective polynomial interpolation problem is maximized. For particular families of segments, we will be able to find explicit solutions of the corresponding maximization problem. The quality of the Fekete segments depends hereby strongly on the utilized normalization of the segmental information in the Vandermonde matrix. To measure the quality of the Fekete segments in interpolation, we analyse the asymptotic behaviour of the generalized Lebesgue constant linked to the interpolation problem. For particular sets of Fekete segments we will get, similar to the nodal case, a favourable logarithmic growth of this constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09378 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Fekete problem in segmental polynomial interpolation Bruno, Ludovico Bruni Erb, Wolfgang Numerical Analysis 41A05, 41A25, A1A30, 65D05 In this article, we study the Fekete problem in segmental and combined nodal-segmental univariate polynomial interpolation by investigating sets of segments, or segments combined with nodes, such that the Vandermonde determinant for the respective polynomial interpolation problem is maximized. For particular families of segments, we will be able to find explicit solutions of the corresponding maximization problem. The quality of the Fekete segments depends hereby strongly on the utilized normalization of the segmental information in the Vandermonde matrix. To measure the quality of the Fekete segments in interpolation, we analyse the asymptotic behaviour of the generalized Lebesgue constant linked to the interpolation problem. For particular sets of Fekete segments we will get, similar to the nodal case, a favourable logarithmic growth of this constant. |
| title | The Fekete problem in segmental polynomial interpolation |
| topic | Numerical Analysis 41A05, 41A25, A1A30, 65D05 |
| url | https://arxiv.org/abs/2403.09378 |