Linear minimum-variance approximants for noisy data
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915688951578624 |
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| author | Ureña, Sergio López Yáñez, Dionisio F. |
| author_facet | Ureña, Sergio López Yáñez, Dionisio F. |
| contents | Inspired by recent developments in subdivision schemes founded on the Weighted Least Squares technique, we construct linear approximants for noisy data in which the weighting strategy minimizes the output variance, thereby establishing a direct correspondence with the Generalized Least Squares and the Minimum-Variance Formulas methodologies. By introducing annihilation-operators for polynomial spaces, we derive usable formulas that are optimal for general correlated non-uniform noise. We show that earlier subdivision rules are optimal for uncorrelated non-uniform noise and, finally, we present numerical evidence to confirm that, in the correlated case, the proposed approximants are better than those currently used in the subdivision literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear minimum-variance approximants for noisy data Ureña, Sergio López Yáñez, Dionisio F. Numerical Analysis Inspired by recent developments in subdivision schemes founded on the Weighted Least Squares technique, we construct linear approximants for noisy data in which the weighting strategy minimizes the output variance, thereby establishing a direct correspondence with the Generalized Least Squares and the Minimum-Variance Formulas methodologies. By introducing annihilation-operators for polynomial spaces, we derive usable formulas that are optimal for general correlated non-uniform noise. We show that earlier subdivision rules are optimal for uncorrelated non-uniform noise and, finally, we present numerical evidence to confirm that, in the correlated case, the proposed approximants are better than those currently used in the subdivision literature. |
| title | Linear minimum-variance approximants for noisy data |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2412.01287 |