IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v466y2024ics0096300323005969.html
   My bibliography  Save this article

Curve fitting by GLSPIA

Author

Listed:
  • Zhuang, Jiayuan
  • Zhu, Yuanpeng
  • Zhong, Jian

Abstract

We develop the generalized B-splines least square progressive iterative approximation (GLSPIA) method to improve LSPIA method (Deng and Lin, 2014) from the perspective of its equivalent neural network framework. We replace the B-spline basis function in standard LSPIA method with the generalized B-spline basis function (Juhász and Róth, 2013) in the GLSPIA method. By adjusting the control points as well as the parameter in the core function, higher precision fitting is achieved. Moreover, in order to solve the over-fitting problem of GLSPIA method when dealing with noise data, we propose three kinds of regularizations using the geometric properties of control polygon. Numerical examples are presented to show the effectiveness of our method.

Suggested Citation

  • Zhuang, Jiayuan & Zhu, Yuanpeng & Zhong, Jian, 2024. "Curve fitting by GLSPIA," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    • Handle: RePEc:eee:apmaco:v:466:y:2024:i:c:s0096300323005969
    DOI: 10.1016/j.amc.2023.128427
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323005969
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.128427?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. Liu, Chengzhi & Liu, Zhongyun & Han, Xuli, 2021. "Preconditioned progressive iterative approximation for tensor product Bézier patches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 372-383.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    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. Liu, Chengzhi & Qiu, Yue & Zhang, Li, 2024. "Preconditioned geometric iterative methods for B-spline interpolation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 87-100.
    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).

    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:466:y:2024:i:c:s0096300323005969. 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.