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

Frank Filbir, Donatella Occorsio and Woula Themistoclakis
Additional contact information
Frank Filbir: Department of Scientific Computing, Helmholtz Zentrum München German Research Center for Environmental Health, 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
Woula Themistoclakis: C.N.R. National Research Council of Italy, IAC Institute for Applied Computing “Mauro Picone”, via P. Castellino, 111, 80131 Napoli, Italy

Mathematics, 2020, vol. 8, issue 4, 1-23

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.

Keywords: Hilbert transform; Hadamard transform; hypersingular integral; Bernstein polynomials; Boolean sum; simultaneous approximation; equidistant nodes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/4/542/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/4/542/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:4:p:542-:d:342244

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().