Approximation of the Hilbert Transform on the unit circle
Numerical Analysis
2024-09-13 v1 Numerical Analysis
Abstract
The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szeg\"o and anti-Szeg\"o 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 Szeg\"o and anti-Szeg\"o formula whose nodes are strategically distanced from the singularity of the Hilbert kernel. Numerical experiments demonstrate the accuracy of the proposed method.
Cite
@article{arxiv.2409.07810,
title = {Approximation of the Hilbert Transform on the unit circle},
author = {Luisa Fermo and Valerio Loi},
journal= {arXiv preprint arXiv:2409.07810},
year = {2024}
}