A general formulation of reweighted least squares fitting

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

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)52-65
Number of pages14
JournalMathematics and Computers in Simulation
Volume225
Early online date7 May 2024
DOIs
Publication statusE-pub ahead of print - 7 May 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.

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