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11 Aug 2025
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
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Ethan Epperly retweeted
Feb 6
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop arxiv.org/abs/2602.05394
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3 Sep 2025
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
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17 Aug 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
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15 Aug 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/2…
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11 Aug 2025
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
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11 Aug 2025
Joint work with my awesome collaborators Tyler Chen, Akash Rao, Raphael Meyer, and Chris Musco!
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5 Aug 2025
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…
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11 Jul 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 @TheSIAMNews for this honor siam.org/publications/siam-n…
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16 Jun 2025
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…
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16 Jun 2025
Also, if you never want to miss a blog post, you can sign up to receive email notifications here! eepurl.com/i5M2P2
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7 Jun 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/2…
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24 May 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/2…
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25 Feb 2025
New blog post with four proofs of the Schur product theorem. Do you know a fifth? ethanepperly.com/index.php/2…
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14 Feb 2025
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/2…
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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. @doescience
@NNSANews
Since 1991, a PhD fellowship that funds researchers using #computationalscience to solve problems in #STEM & those exploring enabling technologies for emerging #HPC systems. Apply for the dual-track #DOECSGF by 1/16/25: bit.ly/48ubGC3 #computerscience #appliedmath
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Ethan Epperly retweeted
8 Nov 2024
Morgane Austern, Lester Mackey: Bounding Hellinger Distance with Stein's Method arxiv.org/abs/2411.04322 arxiv.org/pdf/2411.04322
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26 Dec 2024
The @doecsgf fellowship is the best in the business for PhD students interested in scientific computing. Definitely apply or encourage your students to apply! The application has a few differences from other fellowships; see examples of successful applications below👇
Key dates to note as the #DOECSGF application period winds down:
- 1/14/2025: final submissions due
- 1/23/2025: reference letters due
- 1/31/2025: official transcripts due
Review our webinar recording for additional insight: bit.ly/41iri91
@ENERGY @doescience @NNSANews
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