Work

Approximation of the Hilbert Transform On The Unit Circle

Year: 2025

Type: article

Abstract: The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szegő and anti-Szegő quadrature formulas. These schemes exhibit maximum precision with oppositely signed errors and allow for improved accuracy through their averaged results. Their computation involves a free parameter associated with the corresponding para-orthogonal polynomials. Here, it is suitably chosen to construct a Szegő and anti-Szegő formula whose nodes are strategically distanced from the singularity of the Hilbert kernel. Numerical experiments demonstrate the accuracy of the proposed method.

Source: Journal of Scientific Computing

DOI: 10.1007/s10915-025-03044-3

Authors: Luisa Fermo, Valerio Loi

Institutions: University of Cagliari, University of Insubria

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Gruppo Nazionale per il Calcolo Scientifico