I’m a PhD candidate in Applied and Computational Mathematics at Caltech, whose research is focused on designing computational techniques to solve large-scale linear algebra problems with applications in scientific computing and data science. My advisor is Joel A. Tropp.

I got my undergraduate degrees in Mathematics and Computing from the College of Creative Studies at UCSB, where I worked with Professor Shivkumar Chandrasekaran and the scientific computing group. I have had internships at Sandia National Lab, working with Ryan Sills, Don Ward, and Jonathan Hu; Lawrence Livermore National Lab, working with Andrew Barker; and Lawrence Berkeley National Lab, working with Lin Lin.

I have been recognized for my work with the UCSB Chancellor’s Award for Excellence in Undergraduate Research, the UCSB Mathematics Department’s Raymond L Wilder Award, finalist status for the Hertz foundation fellowship, and the Caltech Thomas A. Tisch Prize for Graduate Teaching in CMS. I grateful to have been supported by the Department of Energy Computational Science Graduate Fellowship.

Recent publications:

**E. N. Epperly**, J. A. Tropp, & R. J. Webber (2024). Embrace rejection: Kernel matrix approximation by accelerated randomly pivoted Cholesky.*arXiv preprint arXiv:2410.03969 [math.NA]*.**E. N. Epperly**(2024). Fast and forward stable randomized algorithms for linear least-squares problems.*SIAM Journal on Matrix Analysis and Applications.*(preprint).- Z. Ding,
**E. N. Epperly**, L. Lin, & R. Zhang (2024). The ESPRIT algorithm under high noise: Optimal error scaling and noisy super-resolution.*Foundations of Computer Science 2024, accepted*. (preprint) **E. N. Epperly**, M. Meier, & Y. Nakatsukasa (2024). Fast randomized least-squares solvers can be just as accurate and stable as classical direct solvers.*arXiv preprint arXiv:2406.03468**[math.NA].*

Some of my favorite projects:

**E. N. Epperly**, J. A. Tropp, & R. J. Webber (2024). XTrace: Making the most of every sample in stochastic trace estimation.(preprint)*SIAM Journal on Matrix Analysis and Applications*.**E. N. Epperly**, L. Lin, & Y. Nakatsukasa (2022). A theory of quantum subspace diagonalization.(preprint)*SIAM Journal of Matrix Analysis and Applications*.- Y. Chen,
**E. N. Epperly**, J. A. Tropp, & R. J. Webber (2022). Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations.*arXiv preprint arXiv:2207.06503 [math.NA]*.