A general formulation of reweighted least squares fitting

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

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 225, issue C, 52-65

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.

Keywords: Weighted least squares; Interpolation; Fitting; Adaptive splines; Hierarchical splines (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:225:y:2024:i:c:p:52-65

DOI: 10.1016/j.matcom.2024.04.029

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