n this paper, we propose a compound scheme of different product integration rules for the simultaneous approximation of both Hilbert and Hadamard transforms of a given function f. The advantages of such a scheme are multiple: a saving in the number of function evaluations and the avoidance of the derivatives of the density function f when approximating the Hadamard transform. Stability and convergence of the proposed method are proved in the space of locally continuous functions in (-1; 1) with possible algebraic singularities at the endpoints, equipped with weighted uniform norms. The theoretical estimates are confirmed by several numerical tests.
SIMULTANEOUS APPROXIMATION OF HILBERT AND HADAMARD TRANSFORMS ON BOUNDED INTERVALS
Mezzanotte D.;Occorsio D.
2024-01-01
Abstract
n this paper, we propose a compound scheme of different product integration rules for the simultaneous approximation of both Hilbert and Hadamard transforms of a given function f. The advantages of such a scheme are multiple: a saving in the number of function evaluations and the avoidance of the derivatives of the density function f when approximating the Hadamard transform. Stability and convergence of the proposed method are proved in the space of locally continuous functions in (-1; 1) with possible algebraic singularities at the endpoints, equipped with weighted uniform norms. The theoretical estimates are confirmed by several numerical tests.File | Dimensione | Formato | |
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