Two new formulas for the numerical evaluation of the Hilbert Transform |
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Authors: | B. Della Vecchia |
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Affiliation: | (1) Dipartimento di Matematica, Istituto G. Castelnuovo, Università di Roma La Sapienza, P. le Aldo Moro 2, I-00185 Roma, Italy |
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Abstract: | We develop two algorithms for the numerical evaluation of the semi-infinite Hilbert Transform of functions with a given algebraic behaviour at the origin and at infinity. The first algorithm is connected with a Gauss-Jacobi type quadrature formula for unbounded intervals; the second is based on a rational Bernstein-type operator. Error estimates for different classes of functions are shown. Finally numerical examples are given, comparing the rules among themselves. |
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Keywords: | 65D32 |
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