Work

Adaptive sparse-knot spline models for approximating sequences of noisy data points in arbitrary-dimensional spaces

Year: 2026

Type: article

Abstract: We address the problem of adaptive approximation of sequences of noisy data points in arbitrary-dimensional spaces using spline models of any degree and smoothness. Knot vectors are determined as solutions of unconstrained sparse optimization problems, yielding a flexible and compact representation based on a limited number of polynomial segments. Unlike previously proposed methods, the resulting knot vectors may include breakpoints with arbitrary multiplicity. Furthermore, the proposed approach enables the reconstruction of both scalar functions and open or closed parametric curves, always relying on a simple, fully unconstrained optimization framework that ensures robustness and computational efficiency.

Source: Computer-Aided Design

DOI: 10.1016/j.cad.2026.104160

Authors: Thierry Bay, Carolina Vittoria Beccari, Lucia Romani, Laura Saini

Institutions: Université Polytechnique Hauts-de-France, University of Bologna, JUNIA

Language: English

Topic: Advanced Numerical Analysis Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,140

Funder: Gruppo Nazionale per il Calcolo Scientifico