Miller research fellow at UC Berkeley. Interested in computational linear algebra he/him
Pasadena, CA
Joined July 2020
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Randomized block Krylov is great at low-rank approximation. But existing analysis gives good results for only large and small block sizes, even though the best block size in practice tends to be in the middle. We resolve this theory-practice gap in arxiv.org/abs/2508.06486
For anyone who wants to learn a bit more computational linear algebra, I highly recommend Tyler Chen’s book on the Lanczos method. Filled to the brim with small delights arxiv.org/abs/2410.11090
More progress by Spielman–Yu which establishes a *1/quasipolynomial lower bound* on the probability of large growth. Taken together, the Urschel/Spielman–Yu results tell an interesting story. The probability of large growth is small but not that small arxiv.org/abs/2610.08701
John Urschel just showed that the growth factor for Gaussian elimination with partial pivoting is ~n^{1/2} with high probability, resolving a long-standing conjecture of Nick Trefethen! arxiv.org/abs/2610.06785
John Urschel just showed that the growth factor for Gaussian elimination with partial pivoting is ~n^{1/2} with high probability, resolving a long-standing conjecture of Nick Trefethen! arxiv.org/abs/2610.06785
Ethan Epperly retweeted
The what now?!
arxiv.org/abs/2610.06783v1
A new “algorithm from the book” today from Chen–Halikias–Musco–Persson. You want a good estimate of the squared Frobenius norm? Generate some Gaussian matrices and form this expression. It gets relative error ε in 4/ε matrix–vector multiplications arxiv.org/abs/2609.28472
The algorithm is called Hutch#. For those in the know, it’s basically Hutch++ but with approximate matrix multiplication instead of low-rank approximation
Ethan Epperly retweeted
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop arxiv.org/abs/2602.05394
New paper out with Chris Camaño, Raphael Meyer, and Joel Tropp re-examining sketching algorithms! Included: subspace injections as an alternative to subspace embeddings, the theory and practice of sparse sketching, tensor sketching, and much more! arxiv.org/abs/2508.21189
Anyone know an easy way of proving the identity 𝔼[g₁²/(g₁²+a²g₂²)] = 1/(1+a) where g₁, g₂ are iid standard Gaussians and a > 0? Ideally, I want an approach that avoids explicitly integrating over the Gaussian/chi-square/F pdf
New blog post out! Vandermonde matrices are famously ill-conditioned, but just how bad are they? In this post, I discuss Gautschi’s 1962 bound showing that Vandermonde matrices are merely exponentially ill-conditioned ethanepperly.com/index.php/2…
New blog post up about the amazingly useful Gaussian integration by parts formula! As an application, we use it to analyze power iteration from a random start ethanepperly.com/index.php/2…
Very excited to share that I’ve been awarded a SIAM student paper prize! I look forward to seeing any of you who will be at #SIAMAN25 in Montréal. Thanks to the committee at @TheSIAMNews for this honor siam.org/publications/siam-n…
New blog post up about the randomized Kaczmarz algorithm. The classic RK algorithms samples rows according to their squared norms, but what happens if you sample them uniformly? The answer surprised me: Uniform sampling is often just as good or even better ethanepperly.com/index.php/2…
Also, if you never want to miss a blog post, you can sign up to receive email notifications here! eepurl.com/i5M2P2
New blog post out about the new Polar Express algorithm of Amsel, Persson, Musco, and Gower for computing the matrix sign function with applications to the Muon optimizer ethanepperly.com/index.php/2…