Accurate algorithms for Bessel matrices
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915107367288832 |
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| author | Delgado, Jorge Orera, Héctor Peña, Juan Manuel |
| author_facet | Delgado, Jorge Orera, Héctor Peña, Juan Manuel |
| contents | In this paper, we prove that any collocation matrix of Bessel polynomials at positive points is strictly totally positive, that is, all its minors are positive. Moreover, an accurate method to construct the bidiagonal factorization of these matrices is obtained and used to compute with high relative accuracy the eigenvalues, singular values and inverses. Similar results for the collocation matrices for the reverse Bessel polynomials are also obtained. Numerical examples illustrating the theoretical results are included. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_10076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accurate algorithms for Bessel matrices Delgado, Jorge Orera, Héctor Peña, Juan Manuel Numerical Analysis 65F05, 65F15, 65G50, 33C10, 33C45, 15A23 In this paper, we prove that any collocation matrix of Bessel polynomials at positive points is strictly totally positive, that is, all its minors are positive. Moreover, an accurate method to construct the bidiagonal factorization of these matrices is obtained and used to compute with high relative accuracy the eigenvalues, singular values and inverses. Similar results for the collocation matrices for the reverse Bessel polynomials are also obtained. Numerical examples illustrating the theoretical results are included. |
| title | Accurate algorithms for Bessel matrices |
| topic | Numerical Analysis 65F05, 65F15, 65G50, 33C10, 33C45, 15A23 |
| url | https://arxiv.org/abs/2501.10076 |