Pivot probabilities and norm effects in Gaussian elimination for $β$-ensembles
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912458726178816 |
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| author | Gunawan, Kenji Peca-Medlin, John |
| author_facet | Gunawan, Kenji Peca-Medlin, John |
| contents | We analyze pivot probabilities in Gaussian elimination with partial pivoting (GEPP) for $2 \times 2$ random matrix ensembles. For GUE matrices, we resolve a previously reported discrepancy between theoretical predictions and empirical observations by deriving the exact pivot probability under standard LAPACK-style implementations. We further show that Dumitriu-Edelman tridiagonal $β$-ensembles agree with the earlier theoretical expectations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pivot probabilities and norm effects in Gaussian elimination for $β$-ensembles Gunawan, Kenji Peca-Medlin, John Probability Numerical Analysis We analyze pivot probabilities in Gaussian elimination with partial pivoting (GEPP) for $2 \times 2$ random matrix ensembles. For GUE matrices, we resolve a previously reported discrepancy between theoretical predictions and empirical observations by deriving the exact pivot probability under standard LAPACK-style implementations. We further show that Dumitriu-Edelman tridiagonal $β$-ensembles agree with the earlier theoretical expectations. |
| title | Pivot probabilities and norm effects in Gaussian elimination for $β$-ensembles |
| topic | Probability Numerical Analysis |
| url | https://arxiv.org/abs/2506.20470 |