Simultaneous approximation of Hilbert and Hadamard transforms on bounded intervals. ETNA - Electronic Transactions on Numerical Analysis
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15 mai 2024
- handle: 10670/1.4l07s9
- issn: 1068-9613
- doi: 10.1553/etna_vol61s28
info:eu-repo/semantics/openAccess
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Domenico Mezzanotte et al., « Simultaneous approximation of Hilbert and Hadamard transforms on bounded intervals. ETNA - Electronic Transactions on Numerical Analysis », Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschafte, ID : 10.1553/etna_vol61s28
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Résumé
In this paper, we propose a compound scheme ofdifferent product integration rules for the simultaneous approximation of bothHilbert and Hadamard transforms of a given function $f$. The advantages ofsuch a scheme are multiple: a saving in the number of function evaluations andthe avoidance of the derivatives of the density function $f$ when approximatingthe Hadamard transform. Stability and convergence of the proposed method areproved in the space of locally continuous functions in $(-1,1)$ with possiblealgebraic singularities at the endpoints, equipped with weighted uniform norms.The theoretical estimates are confirmed by several numerical tests.