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Filbir, F. ; Occorsio, D.* ; Themistoclakis, W.*

Approximation of finite Hilbert and Hadamard transforms by using equally spaced nodes.

Mathematics 8:542 (2020)
Publ. Version/Full Text DOI
Open Access Gold
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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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Publication type Article: Journal article
Document type Scientific Article
Keywords 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
Journal Mathematics
Quellenangaben Volume: 8, Issue: 4, Pages: , Article Number: 542 Supplement: ,
Publisher Mdpi
Publishing Place Basel, Switzerland
Reviewing status