Ethan Epperly
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ethanepperly.bsky.social
Ethan Epperly
@ethanepperly.bsky.social
230 followers 98 following 24 posts
PhD candidate in applied math at Caltech interested in computational linear algebra he/him
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June 16, 2025 at 5:25 PM
ethanepperly.bsky.social
Ack! Typesetting glitch. It was meant to be diag(x) A diag(x) M
We start by computing $x^\top (A\circ M)x$: $$x^\top (A\circ M)x = \sum_{i,j=1}^n x_i (A\circ M)_{ij} x_j = \sum_{i,j=1}^n x_i A_{ij} M_{ij} x_j.$$Now, we may rearrange the sum, use symmetry of $M$, and repackage it as a trace $$x^\top (A\circ M)x = \sum_{i,j=1}^n x_i A_{ij} x_j M_{ji} = \tr(\operatorname{diag}(x) A \operatorname{diag}(x) M).$$This the trace formula for quadratic forms in the Schur product.
February 25, 2025 at 3:45 PM
ethanepperly.bsky.social
Oooo can you share?
December 31, 2024 at 3:34 AM
ethanepperly.bsky.social
Sorry! This is definitely one of the most "advanced" posts I've written on my blog so far. The earlier posts in my "low-rank approximation toolbox" series might be some help, at least! www.ethanepperly.com/index.php/ca...
Low-Rank Approximation Toolbox – Ethan N. Epperly
www.ethanepperly.com
December 9, 2024 at 5:58 PM
ethanepperly.bsky.social
Check out the paper! arxiv.org/abs/2411.19877
Randomized Kaczmarz with tail averaging
The randomized Kaczmarz (RK) method is a well-known approach for solving linear least-squares problems with a large number of rows. RK accesses and processes just one row at a time, leading to exponen...
arxiv.org
December 2, 2024 at 5:06 PM
ethanepperly.bsky.social
The first d columns of an a Haar random matrix from the orthogonal group O(n), yes
November 23, 2024 at 6:07 PM