Smoothed Analysis for the Conjugate Gradient Algorithm
The purpose of this paper is to establish bounds on the rate of convergence of the conjugate gradient algorithm when the underlying matrix is a random positive definite perturbation of a deterministic positive definite matrix. We estimate all finite moments of a natural halting time when the random...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2016 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148528 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Smoothed Analysis for the Conjugate Gradient Algorithm / G. Menon, T. Trogdon // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 22 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | The purpose of this paper is to establish bounds on the rate of convergence of the conjugate gradient algorithm when the underlying matrix is a random positive definite perturbation of a deterministic positive definite matrix. We estimate all finite moments of a natural halting time when the random perturbation is drawn from the Laguerre unitary ensemble in a critical scaling regime explored in Deift et al. (2016). These estimates are used to analyze the expected iteration count in the framework of smoothed analysis, introduced by Spielman and Teng (2001). The rigorous results are compared with numerical calculations in several cases of interest.
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| ISSN: | 1815-0659 |