A general formulation of reweighted least squares fitting

Carlotta Giannelli; Sofia Imperatore; Lisa Maria Kreusser; Estefanía Loayza-Romero; Fatemeh Mohammadi; Nelly Villamizar

doi:10.1016/j.matcom.2024.04.029

A general formulation of reweighted least squares fitting

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

University of Florence
Imperial College London
Swansea University
KU Leuven

Research output: Contribution to journal › Article › peer-review

10 Citations (SciVal)

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.

Original language	English
Pages (from-to)	52-65
Number of pages	14
Journal	Mathematics and Computers in Simulation
Volume	225
Early online date	7 May 2024
DOIs	https://doi.org/10.1016/j.matcom.2024.04.029
Publication status	Published - 30 Nov 2024

Acknowledgements

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. CG and SI are members of the INdAM group GNCS, whose support is gratefully acknowledged.

Funding

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: Dynamics–Geometry–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.

Funders	Funder number
Magdalene College, Cambridge
KU Leuven
Istituto Nazionale di Alta Matematica "Francesco Severi"
Deutsche Forschungsgemeinschaft (DFG)	EXC 2044 –390685587
Deutsche Forschungsgemeinschaft (DFG)
Fonds Wetenschappelijk Onderzoek	G0F5921N, G023721N
Fonds Wetenschappelijk Onderzoek
Engineering and Physical Sciences Research Council	EP/V012835/1
Engineering and Physical Sciences Research Council

Keywords

Adaptive splines
Fitting
Hierarchical splines
Interpolation
Weighted least squares

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Numerical Analysis
Modelling and Simulation
Applied Mathematics

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10.1016/j.matcom.2024.04.029Licence: CC BY

Cite this

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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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A general formulation of reweighted least squares fitting

Abstract

Acknowledgements

Funding

Keywords

ASJC Scopus subject areas

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