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A general formulation of reweighted least squares fitting
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Lisa Maria Kreusser ,
Estefanía Loayza-Romero ,
Fatemeh Mohammadi ,
Nelly Villamizar
Mathematics and Computers in Simulation, Volume: 225, Pages: 52 - 65
Swansea University Author:
Nelly Villamizar
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© 2024 The Author(s). This is an open access article under the CC BY-NC-ND license.
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DOI (Published version): 10.1016/j.matcom.2024.04.029
Abstract
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 spa...
| Published in: | Mathematics and Computers in Simulation |
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| ISSN: | 0378-4754 |
| Published: |
Elsevier BV
2024
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa66448 |
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| Abstract: |
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. |
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| Keywords: |
Weighted least squares; Interpolation; Fitting; Adaptive splines; Hierarchical splines |
| College: |
Faculty of Science and Engineering |
| Funders: |
The authors would like to acknowledge the support provided by the 4th WiSh: Women in Shape Analysis Research Workshop. This collaboration began during the workshop, and we are deeply grateful for the opportunity to work with fellow researchers in the field. CGandSI are members of the INdAM group GNCS, whose support is gratefully acknowledged. LMK acknowledges support from Magdalene College, Cambridge (Nevile Research Fellowship). ELR work was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044–390685587, Mathematics Münster: DynamicsGeometry–Structure. FM was partially supported by the FWO grants (G0F5921N, G023721N), the KU Leuven iBOF/23/064 grant, and the UiT Aurora MASCOT project. NV was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) New Investigator Award EP/V012835/1 |
| Start Page: |
52 |
| End Page: |
65 |