IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v194y2022icp401-415.html
   My bibliography  Save this article

A new approach to deal with C2 cubic splines and its application to super-convergent quasi-interpolation

Author

Listed:
  • Barrera, D.
  • Eddargani, S.
  • Ibáñez, M.J.
  • Lamnii, A.

Abstract

In this paper, we construct a novel normalized B-spline-like representation for C2-continuous cubic spline space defined on an initial partition refined by inserting two new points inside each sub-interval. The basis functions are compactly supported non-negative functions that are geometrically constructed and form a convex partition of unity. With the help of the control polynomial theory introduced herein, a Marsden identity is derived, from which several families of super-convergent quasi-interpolation operators are defined.

Suggested Citation

  • Barrera, D. & Eddargani, S. & Ibáñez, M.J. & Lamnii, A., 2022. "A new approach to deal with C2 cubic splines and its application to super-convergent quasi-interpolation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 401-415.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:401-415
    DOI: 10.1016/j.matcom.2021.12.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421004377
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.12.003?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. Boujraf, A. & Tahrichi, M. & Tijini, A., 2015. "C1 Superconvergent quasi-interpolation based on polar forms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 102-115.
    2. Rahouti, A. & Serghini, A. & Tijini, A., 2020. "Construction of superconvergent quasi-interpolants using new normalized C2 cubic B-splines," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 603-624.
    3. Lamnii, A. & Lamnii, M. & Oumellal, F., 2017. "Computation of Hermite interpolation in terms of B-spline basis using polar forms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 134(C), pages 17-27.
    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. Salah Eddargani & Mohammed Oraiche & Abdellah Lamnii & Mohamed Louzar, 2022. "C 2 Cubic Algebraic Hyperbolic Spline Interpolating Scheme by Means of Integral Values," Mathematics, MDPI, vol. 10(9), pages 1-13, April.

    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. Rahouti, A. & Serghini, A. & Tijini, A., 2020. "Construction of superconvergent quasi-interpolants using new normalized C2 cubic B-splines," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 603-624.
    2. Bouhiri, S. & Lamnii, A. & Lamnii, M. & Zidna, A., 2021. "Quasi-interpolant operators in Bernstein basis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 80-90.

    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:matcom:v:194:y:2022:i:c:p:401-415. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.