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 am supported by a Department of Energy Computational Science Graduate Fellowship.

Recent publications:

**E. N. Epperly**(2023). Fast and forward stable randomized algorithms for linear least-squares problems.*arXiv preprint**arXiv:2311.04362 [math.NA]*.**E. N. Epperly**& E. Moreno (2023). Kernel quadrature with randomly pivoted Cholesky.*NeurIPS 2023*, spotlight. (preprint)- M. Díaz,
**E. N. Epperly**, Z. Frangella, J. A. Tropp, & R. J. Webber (2023). Robust, randomized preconditioning for kernel ridge regression.*arXiv preprint**arXiv:2304.12465 [math.NA]*.

Some of my favorite projects:

**E. N. Epperly**& J. A. Tropp (2024). Efficient error and variance estimation for randomized matrix computations.(preprint)*SIAM Journal on Scientific Computing*.**E. N. Epperly**, J. A. Tropp, & R. J. Webber (2024). XTrace: Making the most of every sample in stochastic trace estimation.(preprint)*SIAM Journal of 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]*.