Research

The less time scientists have to wait for code to run, the more time they can spend thinking about the problems they are tackling. My research aims to develop methods to support the scientists taking on the problems of today.

I’m interested in incorporating probabilistic techniques into classical algorithms to develop methods which are fast and reliable, both in theory and in practice. Right now, I work in the field of numerical linear algebra on Krylov subspace methods such as the conjugate gradient and Lanczos methods. I hope that my work will help to bridge the gap between theoretical computer science and applied computational science.

I am committed to making my research accessible and to facilitating the reproducibility of my work. Please feel free to contact me with any questions or concerns about my research.

I’m advised by Anne Greenbaum and Tom Trogdon.

Publications

More information can be found in my CV. In general, I’ve tried to include descriptions of all my papers which are readable by a broader audience interested in learning about or keeping up with recent advancements in the field.

[6]
Optimal low-memory rational matrix function approximation.
Tyler Chen, Anne Greenbaum, Cameron Musco, Christopher Musco.
@article{lowmem_rational_opt,
    title={Optimal low-memory rational matrix function approximation},
    author={Tyler Chen and Anne Greenbaum and Cameron Musco and Christopher Musco},
    author+an = {1=highlight},
    year={2021},
}
[5]
Error bounds for Lanczos-based matrix function approximation.
Tyler Chen, Anne Greenbaum, Cameron Musco, Christopher Musco.
SIAM Journal on Matrix Analysis, Applications.
@article{lanczos_function_CIF,
    title={Error bounds for Lanczos-based matrix function approximation},
    author={Tyler Chen and Anne Greenbaum and Cameron Musco and Christopher Musco},
    author+an = {1=highlight},
    journal={SIAM Journal on Matrix Analysis and Applications},
    year={2021},
    eprint = {2106.09806},
    archivePrefix = {arXiv},
    primaryClass = {math.NA},
}
[4]
On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic.
Anne Greenbaum, Hexuan Liu, Tyler Chen.
SIAM Journal on Scientific Computing.
@article{cg_variants_convergence_rates,
    doi = {10.1137/20m1346249},
    year = {2021},
    month = jul,
    publisher = {Society for Industrial {\&} Applied Mathematics (SIAM)},
    pages = {S496--S515},
    author = {Anne Greenbaum and Hexuan Liu and Tyler Chen},
    title = {On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic},
    journal = {SIAM Journal on Scientific Computing},
    eprint = {1905.05874},
    archivePrefix = {arXiv},
    primaryClass = {cs.NA},
}
[3]
Analysis of stochastic Lanczos quadrature for spectrum approximation.
Tyler Chen, Thomas Trogdon, Shashanka Ubaru.
Proceedings of the 38th International Conference on Machine Learning.
@inproceedings{slq_analysis,
    title={Analysis of stochastic Lanczos quadrature for spectrum approximation},
    author={Tyler Chen and Thomas Trogdon and Shashanka Ubaru},
    author+an = {1=highlight},
    booktitle = 	 {Proceedings of the 38th International Conference on Machine Learning},
    pages = 	 {1728--1739},
    year = 	 {2021},
    editor = 	 {Meila, Marina and Zhang, Tong},
    volume = 	 {139},
    series = 	 {Proceedings of Machine Learning Research},
    month = 	 {18--24 Jul},
    publisher =    {PMLR},
    url = 	 {http://proceedings.mlr.press/v139/chen21s.html},
    eprint={2105.06595},
    archivePrefix={arXiv},
    primaryClass={cs.DS},
}
[2]
Non-asymptotic moment bounds for random variables rounded to non-uniformly spaced sets.
Tyler Chen.
Stat.
@article{finite_precision_random_variables,
    title = {Non-asymptotic moment bounds for random variables rounded to non-uniformly spaced sets},
    author = {Tyler Chen},
    author+an = {1=highlight},
    doi = {10.1002/STA4.395},
    year = {2021},
    month = {june},
    publisher = {Wiley},
    volume = {},
    number = {},
    pages = {e395},
    journal = {Stat},
    eprint = {2007.11041},
    archivePrefix = {arXiv},
    primaryClass = {math.ST},
}
[1]
Predict-and-recompute conjugate gradient variants.
Tyler Chen, Erin C. Carson.
SIAM Journal on Scientific Computing.
@article{predict_and_recompute,
    title={Predict-and-recompute conjugate gradient variants},
    author={Tyler Chen and Erin C. Carson},
    author+an = {1=highlight},
    doi = {10.1137/19m1276856},
    year = {2020},
    month = jan,
    publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
    volume = {42},
    number = {5},
    pages = {A3084--A3108},
    journal = {SIAM Journal on Scientific Computing},
    eprint={1905.01549},
    archivePrefix={arXiv},
    primaryClass={cs.NA},
}

Here are links to my Google Scholar profile and ORCID: 0000-0002-1187-1026.

Collaboration

I’m always interested in finding things to collaborate on (and people to collaborate with).

If you’re an undergrad student interested in research or grad school, please feel free to reach out; I’d be happy to try to help you find something to work on! You may also be interested in the Washington Directed Reading Program as well as the Women in Applied Mathematics Mentorship Program.

Introductions to some topics I think are interesting