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Nonlinear least-squares spline fitting with variable knots

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  • Kovács, Péter
  • Fekete, Andrea M.

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.

Suggested Citation

  • Kovács, Péter & Fekete, Andrea M., 2019. "Nonlinear least-squares spline fitting with variable knots," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 490-501.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:490-501
    DOI: 10.1016/j.amc.2019.02.051
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    References listed on IDEAS

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    1. Dianne O’Leary & Bert Rust, 2013. "Variable projection for nonlinear least squares problems," Computational Optimization and Applications, Springer, vol. 54(3), pages 579-593, April.
    2. Molinari, Nicolas & Durand, Jean-Francois & Sabatier, Robert, 2004. "Bounded optimal knots for regression splines," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 159-178, March.
    3. Yuan Yuan & Nan Chen & Shiyu Zhou, 2013. "Adaptive B-spline knot selection using multi-resolution basis set," IISE Transactions, Taylor & Francis Journals, vol. 45(12), pages 1263-1277.
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    Cited by:

    1. Zhuang, Jiayuan & Zhu, Yuanpeng & Zhong, Jian, 2024. "Curve fitting by GLSPIA," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    2. Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Lattuada, Andrea & Verrall, Richard J., 2023. "Geometrically designed variable knot splines in generalized (non-)linear models," Applied Mathematics and Computation, Elsevier, vol. 436(C).

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