Approximation of the Hilbert Transform on the unit circle
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910601654042624 |
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| author | Fermo, Luisa Loi, Valerio |
| author_facet | Fermo, Luisa Loi, Valerio |
| contents | The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szegö and anti-Szegö 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 Szegö and anti-Szegö formula whose nodes are strategically distanced from the singularity of the Hilbert kernel. Numerical experiments demonstrate the accuracy of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation of the Hilbert Transform on the unit circle Fermo, Luisa Loi, Valerio Numerical Analysis 65D30, 42A10, 30E20, 32A55 The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szegö and anti-Szegö 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 Szegö and anti-Szegö formula whose nodes are strategically distanced from the singularity of the Hilbert kernel. Numerical experiments demonstrate the accuracy of the proposed method. |
| title | Approximation of the Hilbert Transform on the unit circle |
| topic | Numerical Analysis 65D30, 42A10, 30E20, 32A55 |
| url | https://arxiv.org/abs/2409.07810 |