Ethan Epperly

PhD candidate in applied math @Caltech and @doecsgf fellow interested in computational linear algebra he/him

[Ethan Epperly @ethanepperly]

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 https://t.co/iYTshDEGXv

[Daniel Kressner @_kreda_]

Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop https://t.co/Ap2keEQGKr

[Damek @damekdavis]

cool paper @ethanepperly!

[Ethan Epperly @ethanepperly]

@angeris @damekdavis Hm. Not sure you’re on base here. I assume you’re talking about Bubeck §3.5 stuff? We study Ax=b when A is not pd. So matrix-vector products are not gradients of a convex quadratic. A similar result is known for Krylov algorithms, but we bound against arbitrary rand algorithms

[Ethan Epperly @ethanepperly]

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! https://t.co/gq6z1CKsRW

[Ethan Epperly @ethanepperly]

@magoghm Seems correct but also still uses a lot of explicit integrals, which I’m hoping to avoid…

[Ethan Epperly @ethanepperly]

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

[Ethan Epperly @ethanepperly]

@PengLiangzu This is a nice solution. Somehow, still isn’t quite what I’m after. I’m really hoping for a simple direct argument that uses properties of the Gaussian distribution rather than known relations to other distributions

[Ethan Epperly @ethanepperly]

@mathlfs The full version of Gautschi’s bound is attained if all the locations are in a ray on the complex plane. So that shows the exponential scaling is tight. I don’t know of any lower bounds for arbitrary locations

[Ethan Epperly @ethanepperly]

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 https://t.co/2IZNfNVrw3

[Ethan Epperly @ethanepperly]

Joint work with my awesome collaborators Tyler Chen, Akash Rao, Raphael Meyer, and Chris Musco!

[Ethan Epperly @ethanepperly]

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 https://t.co/iYTshDEGXv

[Ethan Epperly @ethanepperly]

@humphilomath @jwt0625 That’s a depressing thought…

[Ethan Epperly @ethanepperly]

@miniapeur It’s the easy direction of Stein’s lemma. I really regard Stein’s lemma as the converse to this result

[Ethan Epperly @ethanepperly]

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 https://t.co/Wi9r9iGtnn

[Ethan Epperly @ethanepperly]

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 https://t.co/2dIIW3YRXO

[Ethan Epperly @ethanepperly]

Reflections on five years of blogging https://t.co/U3kgnAoQhO

[Ethan Epperly @ethanepperly]

@MarkSchmidtUBC Thanks for the reference. I’ve added the paper to the post!

[Ethan Epperly @ethanepperly]

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 https://t.co/8wQvFcURi5

[Ethan Epperly @ethanepperly]

@gautamcgoel Thanks!

[Ethan Epperly @ethanepperly]

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