On the Lebesgue constant of the Morrow-Patterson points
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909434043695104 |
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| author | Beberok, Tomasz Białas-Cież, Leokadia De Marchi, Stefano |
| author_facet | Beberok, Tomasz Białas-Cież, Leokadia De Marchi, Stefano |
| contents | The study of interpolation nodes and their associated Lebesgue constants are central to numerical analysis, impacting the stability and accuracy of polynomial approximations. In this paper, we will explore the Morrow-Patterson points, a set of interpolation nodes introduced to construct cubature formulas of a minimum number of points in the square for a fixed degree $n$. We prove that their Lebesgue constant growth is ${\cal O}(n^2)$ as was conjectured based on numerical evidence about twenty years ago in the paper by Caliari, M., De Marchi, S., Vianello, M., {\it Bivariate polynomial interpolation on the square at new nodal sets}, Appl. Math. Comput. 165(2) (2005), 261--274. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14595 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Lebesgue constant of the Morrow-Patterson points Beberok, Tomasz Białas-Cież, Leokadia De Marchi, Stefano Numerical Analysis Classical Analysis and ODEs The study of interpolation nodes and their associated Lebesgue constants are central to numerical analysis, impacting the stability and accuracy of polynomial approximations. In this paper, we will explore the Morrow-Patterson points, a set of interpolation nodes introduced to construct cubature formulas of a minimum number of points in the square for a fixed degree $n$. We prove that their Lebesgue constant growth is ${\cal O}(n^2)$ as was conjectured based on numerical evidence about twenty years ago in the paper by Caliari, M., De Marchi, S., Vianello, M., {\it Bivariate polynomial interpolation on the square at new nodal sets}, Appl. Math. Comput. 165(2) (2005), 261--274. |
| title | On the Lebesgue constant of the Morrow-Patterson points |
| topic | Numerical Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2412.14595 |