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Author

Ethan N. Epperly

University of California, Berkeley

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Preprint Aug 2026

A new analysis of the randomly pivoted Cholesky algorithm

The randomly pivoted Cholesky algorithm is one of the leading methods for computing a low-rank approximation to a large positive-semidefinite matrix. However, while it consistently achieves accuracy comparable to or better than competing methods of its type in experiments, its theoretical analysis lags somewhat behind...

Ethan N. Epperly · 0 citations
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

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