Well-Conditioned Oblivious Perturbations in Linear Space
Perturbing a deterministic $n$-dimensional matrix with small Gaussian noise is a cornerstone of smoothed analysis of algorithms [Spielman and Teng, JACM 2004], as it reduces the condition number of the input to $O(n)$, and with it the complexity of many matrix algorithms. However, when deployed algorithmically, these perturbations are expensive due to the cost of generating and storing $n^2$ Gaussian random variables. We propose a perturbation that requires generating and storing $O(n)$ random numbers in $O(\log n)$ bits of precision, and reduces the condition number of any deterministic matrix to $O(n)$, matching Gaussian perturbations. Our result in particular implies a better complexit...
| Authors | Shabarish Chenakkod, Michał Dereziński, Xiaoyu Dong et al. |
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| Primary category | cs.DS |
| Published | 25 April 2026 |
| Last updated at source | 25 April 2026 |
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