Author

Aaron Tian

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Preprint Aug 2026

Fast Length-Squared Sampling for Positive-Semidefinite Matrices

We describe a simple rejection-sampling-based algorithm to perform length-squared sampling on an $n \times n$ positive-semidefinite (psd) matrix: that is, to sample a column with probability proportional to its squared $\ell_2$-norm. The algorithm runs in just $O(n)$ expected time, which is significantly sublinear in t...

Rajarshi Bhattacharjee, Ethan N. Epperly, Cameron Musco et al. · 0 citations