IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i4p542-d342244.html
   My bibliography  Save this article

Approximation of Finite Hilbert and Hadamard Transforms by Using Equally Spaced Nodes

Author

Listed:
  • Frank Filbir

    (Department of Scientific Computing, Helmholtz Zentrum München German Research Center for Environmental Health, Ingolstädter Landstrasse 1, 85764 Neuherberg, Germany
    Applied Numerical Analysis, Fakultät für Mathematik, Technische Universität München, Boltzmannstrasse 3 85748 Garching bei München. Research Center, Ingolstädter Landstrasse 1, 85764 Neuherberg, Germany)

  • Donatella Occorsio

    (Department of Mathematics, Computer Science and Economics, University of Basilicata, viale dell’Ateneo Lucano 10, 85100 Potenza, Italy
    C.N.R. National Research Council of Italy, IAC Institute for Applied Computing “Mauro Picone”, via P. Castellino, 111, 80131 Napoli, Italy)

  • Woula Themistoclakis

    (C.N.R. National Research Council of Italy, IAC Institute for Applied Computing “Mauro Picone”, via P. Castellino, 111, 80131 Napoli, Italy)

Abstract

In the present paper, we propose a numerical method for the simultaneous approximation of the finite Hilbert and Hadamard transforms of a given function f , supposing to know only the samples of f at equidistant points. As reference interval we consider [ − 1 , 1 ] and as approximation tool we use iterated Boolean sums of Bernstein polynomials, also known as generalized Bernstein polynomials. Pointwise estimates of the errors are proved, and some numerical tests are given to show the performance of the procedures and the theoretical results.

Suggested Citation

  • Frank Filbir & Donatella Occorsio & Woula Themistoclakis, 2020. "Approximation of Finite Hilbert and Hadamard Transforms by Using Equally Spaced Nodes," Mathematics, MDPI, vol. 8(4), pages 1-23, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:542-:d:342244
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/4/542/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/4/542/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:8:y:2020:i:4:p:542-:d:342244. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.