$L^2$ and $L^\infty$ rational approximation
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| Format: | Preprint |
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2025
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| _version_ | 1866914223662039040 |
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| author | Ackermann, Michael S. Reiter, Sean Trefethen, Lloyd N. |
| author_facet | Ackermann, Michael S. Reiter, Sean Trefethen, Lloyd N. |
| contents | Using recently developed algorithms, we compute and compare best $L^2$ and $L^\infty$ rational approximations of analytic functions on the unit disk. Although there is some theory for these problems going back decades, this may be the first computational study. To compute the $L^2$ best approximations, we employ a new formulation of TF-IRKA in barycentric form. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_23357 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L^2$ and $L^\infty$ rational approximation Ackermann, Michael S. Reiter, Sean Trefethen, Lloyd N. Numerical Analysis Complex Variables 41A20, 65D15 Using recently developed algorithms, we compute and compare best $L^2$ and $L^\infty$ rational approximations of analytic functions on the unit disk. Although there is some theory for these problems going back decades, this may be the first computational study. To compute the $L^2$ best approximations, we employ a new formulation of TF-IRKA in barycentric form. |
| title | $L^2$ and $L^\infty$ rational approximation |
| topic | Numerical Analysis Complex Variables 41A20, 65D15 |
| url | https://arxiv.org/abs/2512.23357 |