Morgane Austern, Lester Mackey: Bounding Hellinger Distance with Stein's Method arxiv.org/abs/2411.04322 arxiv.org/pdf/2411.04322

Short Stories: "Rational Approximation" (by Lloyd N. Trefethen, in Notices of the American Mathematical Society): ams.org/journals/notic…

New preprint with Alice Cortinovis with some of the best (probabilistic) bounds for DEIM et al.

TODAY is the day! #DOECSGF applications must be submitted via the online system by 5 p.m. CT. Direct questions to csgf[at]krellinst[dot]org. Reference letters are due 1/23 & transcripts by 1/31. Thank you for your interest & best of luck to all candidates. DOE Office of Science NNSA

New blog post up! In it, I look at the question: how accurate is sketch-and-solve method for least squares? A standard bound suggests the residual is within a 1 + O(η) factor of optimal for an embedding of distortion η. But this isn't the correct answer! ethanepperly.com/index.php/2025…

New blog post with four proofs of the Schur product theorem. Do you know a fifth? ethanepperly.com/index.php/2025…

New blog post out in my series on Markov chains! In this post, I discuss Poincaré inequalities and their connection to mixing of Markov chains ethanepperly.com/index.php/2025…

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/2025…

Reflections on five years of blogging ethanepperly.com/index.php/2025…

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 SIAM for this honor siam.org/publications/s…

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/2025…

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/2025…

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 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