Nonlinear least-squares spline fitting with variable knots

Péter Kovács and Andrea M. Fekete

Applied Mathematics and Computation, 2019, vol. 354, issue C, 490-501

Abstract: In this paper, we present a nonlinear least-squares fitting algorithm using B-splines with free knots. Since its performance strongly depends on the initial estimation of the free parameters (i.e. the knots), we also propose a fast and efficient knot-prediction algorithm that utilizes numerical properties of first-order B-splines. Using ℓp(p=1,2,∞) norm solutions, we also provide three different strategies for properly selecting the free knots. Our initial predictions are then iteratively refined by means of a gradient-based variable projection optimization. Our method is general in nature and can be used to estimate the optimal number of knots in cases in which no a-priori information is available.

Keywords: Free knot splines; Nonlinear nonconvex optimization; Variable projection; Nonlinear least-squares problems; Signal compression; Electrocardiograms (ECG) (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:354:y:2019:i:c:p:490-501

DOI: 10.1016/j.amc.2019.02.051

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