Constrained mock-Chebyshev least squares approximation for Hermite interpolation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929487695839232 |
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| author | Dell'Accio, Francesco Marcellán, Francisco Nudo, Federico |
| author_facet | Dell'Accio, Francesco Marcellán, Francisco Nudo, Federico |
| contents | This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from the Runge phenomenon. To mitigate this issue, we propose an extension of the constrained mock-Chebyshev least squares approximation technique to Hermite interpolation. This approach leverages both function and derivative evaluations, resulting in more accurate approximations. Numerical experiments are implemented in order to illustrate the effectiveness of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constrained mock-Chebyshev least squares approximation for Hermite interpolation Dell'Accio, Francesco Marcellán, Francisco Nudo, Federico Numerical Analysis 41A05, 41A10 This paper addresses the challenge of function approximation using Hermite interpolation on equally spaced nodes. In this setting, standard polynomial interpolation suffers from the Runge phenomenon. To mitigate this issue, we propose an extension of the constrained mock-Chebyshev least squares approximation technique to Hermite interpolation. This approach leverages both function and derivative evaluations, resulting in more accurate approximations. Numerical experiments are implemented in order to illustrate the effectiveness of the proposed method. |
| title | Constrained mock-Chebyshev least squares approximation for Hermite interpolation |
| topic | Numerical Analysis 41A05, 41A10 |
| url | https://arxiv.org/abs/2409.03357 |