Small singular values can increase in lower precision
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929249590444032 |
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| author | Boutsikas, Christos Drineas, Petros Ipsen, Ilse C. F. |
| author_facet | Boutsikas, Christos Drineas, Petros Ipsen, Ilse C. F. |
| contents | We perturb a real matrix $A$ of full column rank, and derive lower bounds for the smallest singular values of the perturbed matrix, in terms of normwise absolute perturbations. Our bounds, which extend existing lower-order expressions, demonstrate the potential increase in the smallest singular values, and represent a qualitative model for the increase in the small singular values after a matrix has been downcast to a lower arithmetic precision. Numerical experiments confirm the qualitative validity of this model and its ability to predict singular values changes in the presence of decreased arithmetic precision. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03547 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Small singular values can increase in lower precision Boutsikas, Christos Drineas, Petros Ipsen, Ilse C. F. Numerical Analysis 65F15, 65G50, 15A18, 15A23, 15A42 We perturb a real matrix $A$ of full column rank, and derive lower bounds for the smallest singular values of the perturbed matrix, in terms of normwise absolute perturbations. Our bounds, which extend existing lower-order expressions, demonstrate the potential increase in the smallest singular values, and represent a qualitative model for the increase in the small singular values after a matrix has been downcast to a lower arithmetic precision. Numerical experiments confirm the qualitative validity of this model and its ability to predict singular values changes in the presence of decreased arithmetic precision. |
| title | Small singular values can increase in lower precision |
| topic | Numerical Analysis 65F15, 65G50, 15A18, 15A23, 15A42 |
| url | https://arxiv.org/abs/2303.03547 |