A general formulation of reweighted least squares fitting
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911828406173696 |
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| author | Giannelli, Carlotta Imperatore, Sofia Kreusser, Lisa Maria Loayza-Romero, Estefanía Mohammadi, Fatemeh Villamizar, Nelly |
| author_facet | Giannelli, Carlotta Imperatore, Sofia Kreusser, Lisa Maria Loayza-Romero, Estefanía Mohammadi, Fatemeh Villamizar, Nelly |
| contents | We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when the solution is sought in any finite-dimensional vector space; secondly, to provide a general strategy to iteratively update the weights according to the approximation error and apply it to the spline fitting problem. In the experiments, we provide numerical examples for the case of polynomials and splines spaces. Subsequently, we evaluate the performance of our fitting scheme for spline curve and surface approximation, including adaptive spline constructions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03742 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A general formulation of reweighted least squares fitting Giannelli, Carlotta Imperatore, Sofia Kreusser, Lisa Maria Loayza-Romero, Estefanía Mohammadi, Fatemeh Villamizar, Nelly Numerical Analysis We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when the solution is sought in any finite-dimensional vector space; secondly, to provide a general strategy to iteratively update the weights according to the approximation error and apply it to the spline fitting problem. In the experiments, we provide numerical examples for the case of polynomials and splines spaces. Subsequently, we evaluate the performance of our fitting scheme for spline curve and surface approximation, including adaptive spline constructions. |
| title | A general formulation of reweighted least squares fitting |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2404.03742 |