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Approximation of finite Hilbert and Hadamard transforms by using equally spaced nodes.
Mathematics 8:542 (2020)
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.
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Publikationstyp
Artikel: Journalartikel
Dokumenttyp
Wissenschaftlicher Artikel
Schlagwörter
Hilbert Transform ; Hadamard Transform ; Hypersingular Integral ; Bernstein Polynomials ; Boolean Sum ; Simultaneous Approximation ; Equidistant Nodes; Numerical Evaluation; Integral-equations; Bernstein; Operators
ISSN (print) / ISBN
2227-7390
e-ISSN
2227-7390
Zeitschrift
Mathematics
Quellenangaben
Band: 8,
Heft: 4,
Artikelnummer: 542
Verlag
MDPI
Verlagsort
Basel, Switzerland
Nichtpatentliteratur
Publikationen
Begutachtungsstatus
Peer reviewed
Institut(e)
Institute of Computational Biology (ICB)