IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v354y2019icp490-501.html
   My bibliography  Save this article

Nonlinear least-squares spline fitting with variable knots

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319301559
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.02.051?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zheng, Sanpeng & Feng, Renzhong, 2023. "A variable projection method for the general radial basis function neural network," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    2. Basna, Rani & Nassar, Hiba & Podgórski, Krzysztof, 2022. "Data driven orthogonal basis selection for functional data analysis," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Gálvez, Akemi & Iglesias, Andrés, 2016. "Particle-based meta-model for continuous breakpoint optimization in smooth local-support curve fitting," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 195-212.
    4. Maximilian S. Ernst & Aaron Peikert & Andreas M. Brandmaier & Yves Rosseel, 2023. "A Note on the Connection Between Trek Rules and Separable Nonlinear Least Squares in Linear Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 98-116, March.
    5. Stolbunov, Valentin & Nair, Prasanth B., 2018. "Sparse radial basis function approximation with spatially variable shape parameters," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 170-184.
    6. Marius Yapo & Jie He & Bruno Gagnon & Luc Savard & Roland Leduc, 2015. "La valeur économique pour l’amélioration de la qualité de l’eau: le cas de la rivière Magog et du lac Magog (Québec, Canada)," Cahiers de recherche 15-15, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    7. Adelina Bärligea & Philipp Hochstaffl & Franz Schreier, 2023. "A Generalized Variable Projection Algorithm for Least Squares Problems in Atmospheric Remote Sensing," Mathematics, MDPI, vol. 11(13), pages 1-20, June.
    8. Binder, Harald & Sauerbrei, Willi, 2008. "Increasing the usefulness of additive spline models by knot removal," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5305-5318, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:490-501. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.