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A general formulation of reweighted least squares fitting

Carlotta Giannelli, Sofia Imperatore Orcid Logo, Lisa Maria Kreusser Orcid Logo, Estefanía Loayza-Romero Orcid Logo, Fatemeh Mohammadi Orcid Logo, Nelly Villamizar Orcid Logo

Mathematics and Computers in Simulation, Volume: 225, Pages: 52 - 65

Swansea University Author: Nelly Villamizar Orcid Logo

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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...

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Published in: Mathematics and Computers in Simulation
ISSN: 0378-4754
Published: Elsevier BV 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa66448
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spelling 2024-09-19T10:46:12.2784342 v2 66448 2024-05-16 A general formulation of reweighted least squares fitting 41572bcee47da6ba274ecd1828fbfef4 0000-0002-8741-7225 Nelly Villamizar Nelly Villamizar true false 2024-05-16 MACS 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. Journal Article Mathematics and Computers in Simulation 225 52 65 Elsevier BV 0378-4754 Weighted least squares; Interpolation; Fitting; Adaptive splines; Hierarchical splines 1 11 2024 2024-11-01 10.1016/j.matcom.2024.04.029 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Another institution paid the OA fee 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 2024-09-19T10:46:12.2784342 2024-05-16T10:13:30.7044083 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Carlotta Giannelli 1 Sofia Imperatore 0009-0003-9116-9978 2 Lisa Maria Kreusser 0000-0002-1131-1125 3 Estefanía Loayza-Romero 0000-0001-7919-9259 4 Fatemeh Mohammadi 0000-0001-5187-0995 5 Nelly Villamizar 0000-0002-8741-7225 6 66448__31372__f4b66872f40a4b919b1ea0836e681ccd.pdf 66448.VoR.pdf 2024-09-19T10:43:42.7905867 Output 2359192 application/pdf Version of Record true © 2024 The Authors. This is an open access article under the CC BY license. true eng http://creativecommons.org/licenses/by/4.0/
title A general formulation of reweighted least squares fitting
spellingShingle A general formulation of reweighted least squares fitting
Nelly Villamizar
title_short A general formulation of reweighted least squares fitting
title_full A general formulation of reweighted least squares fitting
title_fullStr A general formulation of reweighted least squares fitting
title_full_unstemmed A general formulation of reweighted least squares fitting
title_sort A general formulation of reweighted least squares fitting
author_id_str_mv 41572bcee47da6ba274ecd1828fbfef4
author_id_fullname_str_mv 41572bcee47da6ba274ecd1828fbfef4_***_Nelly Villamizar
author Nelly Villamizar
author2 Carlotta Giannelli
Sofia Imperatore
Lisa Maria Kreusser
Estefanía Loayza-Romero
Fatemeh Mohammadi
Nelly Villamizar
format Journal article
container_title Mathematics and Computers in Simulation
container_volume 225
container_start_page 52
publishDate 2024
institution Swansea University
issn 0378-4754
doi_str_mv 10.1016/j.matcom.2024.04.029
publisher Elsevier BV
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
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description 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.
published_date 2024-11-01T08:35:52Z
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score 11.048388

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