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. © 1994 BIT Foundation.
Two new formulas for the numerical evaluation of the Hilbert Transform / DELLA VECCHIA, Biancamaria. - In: BIT. - ISSN 0006-3835. - STAMPA. - 34:3(1994), pp. 346-360. [10.1007/bf01935644]
Two new formulas for the numerical evaluation of the Hilbert Transform
DELLA VECCHIA, Biancamaria
1994
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. © 1994 BIT Foundation.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
