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Convergence and stability of a new quadrature rule for evaluating Hilbert transform

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Abstract

The importance of singular integral transforms, coming from their many applications, justifies some interest in their numerical approximation. Here we propose a stable and convergent algorithm to evaluate such transforms on the real line. Numerical examples confirming the theoretical results are given.

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Authors and Affiliations

  1. Sezione di Napoli, CNR - Istituto per le Applicazioni del Calcolo “Mauro Picone”, Via Pietro Castellino 111, 80131, Napoli, Italy

    M. R. Capobianco

  2. Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli “Federico II”, Complesso Monte Sant’Angelo, Edificio T, Via Cintia, 80126, Napoli, Italy

    G. Criscuolo

Authors
  1. M. R. Capobianco
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  2. G. Criscuolo
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Correspondence to M. R. Capobianco.

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Capobianco, M.R., Criscuolo, G. Convergence and stability of a new quadrature rule for evaluating Hilbert transform. Numer Algor 60, 579–592 (2012). https://doi.org/10.1007/s11075-012-9584-8

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  • DOI: https://doi.org/10.1007/s11075-012-9584-8

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