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On the evaluation of Hilbert transforms by means of a particular class of Turán quadrature rules

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Abstract

A method for evaluating Hilbert transforms, by means of Turán quadrature rules with generalized Gegenbauer weights, is presented. The main feature of these integration formulas is the independence of the nodes of their multiplicity and thus of the precision degree. The error is analyzed both from a real and a complex perspective; in this context a new representation of the remainder term of the quadrature rules with multiple nodes for the evaluation of Hilbert transforms, valid not only for the particular class of weight functions here considered, is presented. A few numerical examples are provided.

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Authors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università “La Sapienza”, Roma, Italy

    Laura Gori

  2. Dipartimento di Energetica, Università di L'Aquila, Italy

    Elisabetta Santi

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  1. Laura Gori
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  2. Elisabetta Santi
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Work sponsored by Ministero della Ricerca Scientifica e Tecnologia, Italy.

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Gori, L., Santi, E. On the evaluation of Hilbert transforms by means of a particular class of Turán quadrature rules. Numer Algor 10, 27–39 (1995). https://doi.org/10.1007/BF02198294

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