IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v307y2017icp113-123.html
   My bibliography  Save this article

Kernel-based adaptive approximation of functions with discontinuities

Author

Listed:
  • Lenarduzzi, Licia
  • Schaback, Robert

Abstract

One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth in certain subdomains will have good approximations in those subdomains, and these sub-approximations can possibly be calculated efficiently in parallel, as long as the subdomains do not overlap. This paper proposes an algorithm that first calculates sub-approximations on non-overlapping subdomains, then extends the subdomains as much as possible and finally produces a global solution on the given domain by letting the subdomains fill the whole domain. Consequently, there will be no Gibbs phenomenon along the boundaries of the subdomains. The method detects faults and gradient faults with good accuracy. Throughout, the algorithm works for fixed scattered input data of the function itself, not on spectral data, and it does not resample.

Suggested Citation

  • Lenarduzzi, Licia & Schaback, Robert, 2017. "Kernel-based adaptive approximation of functions with discontinuities," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 113-123.
    • Handle: RePEc:eee:apmaco:v:307:y:2017:i:c:p:113-123
    DOI: 10.1016/j.amc.2017.02.043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317301546
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.02.043?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. López de Silanes, María Cruz & Parra, María Cruz & Torrens, Juan José, 2008. "On a new characterization of finite jump discontinuities and its application to vertical fault detection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(2), pages 247-256.
    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. Aràndiga, Francesc & Donat, Rosa & Romani, Lucia & Rossini, Milvia, 2020. "On the reconstruction of discontinuous functions using multiquadric RBF–WENO local interpolation techniques," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 4-24.

    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. Izquierdo, Diego & de Silanes, María Cruz López & Parra, María Cruz & Torrens, Juan José, 2014. "CS-RBF interpolation of surfaces with vertical faults from scattered data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 102(C), pages 11-23.

    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:307:y:2017:i:c:p:113-123. 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.