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 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.

This page contains a collection of the things I’ve been working on recently. In general, I try to include a description of papers which are readable by a broader audience interested in learning about or keeping up with recent advancements in the field. I also have some short introductory pieces on topics I think are interesting.

Publications

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

[4]
Error bounds for the Lanczos algorithm for function approximation.
Tyler Chen, Anne Greenbaum, Cameron Musco, Christopher Musco.
@article{lanczos_error_bounds,
    title = {Error bounds for the Lanczos algorithm for function approximation},
    author = {Tyler Chen, Anne Greenbaum, Cameron Musco, Christopher Musco},
    year = {},
}
[3]
Rounding Random Variables to Finite Precision.
Tyler Chen.
@article{finite_precision_random_variables,
    title = {Rounding Random Variables to Finite Precision},
    author = {Tyler Chen},
    year = {2020},
    eprint = {2007.11041},
    archivePrefix = {arXiv},
    primaryClass = {math.ST},
}
[2]
Predict-and-recompute conjugate gradient variants.
Tyler Chen, Erin C. Carson.
@article{predict_and_recompute_cg,
    title={Predict-and-recompute conjugate gradient variants},
    author={Tyler Chen and Erin C. Carson},
    year={2020},
    eprint={1905.01549},
    archivePrefix={arXiv},
    primaryClass={cs.NA},
}
[1]
On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic.
Anne Greenbaum, Hexuan Liu, Tyler Chen.
@article{cg_variants_convergence_rates,
    title = {On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic},
    author = {Anne Greenbaum and Hexuan Liu and Tyler Chen},
    year = {2019},
    eprint = {1905.05874},
    archivePrefix = {arXiv},
    primaryClass = {cs.NA},
}

Talks and Posters

[4]
Analyzing the Effects of Local Roundoff Error on Predict-and-Recompute Conjugate Gradient Variants.
Tyler Chen, Erin C. Carson, Anne Greenbaum.
Poster at XXI Householder. (Canceled).
@misc{predict_and_recompute_HH20,
    title = {Analyzing the Effects of Local Roundoff Error on Predict-and-Recompute Conjugate Gradient Variants},
    author = {Tyler Chen, Erin C. Carson, Anne Greenbaum},
    author+an = {1=highlight},
    month = {June},
    year = {2020},
    note = {Poster at XXI Householder. (Canceled)},
}
[3]
Predict-and-recompute conjugate gradient variants.
Tyler Chen.
Presentation at Copper Mountain Student Paper Award Session. (Canceled).
@misc{predict_and_recompute_CM20,
    title = {Predict-and-recompute conjugate gradient variants},
    author = {Tyler Chen},
    author+an = {1=highlight},
    month = {March},
    year = {2020},
    note = {Presentation at Copper Mountain Student Paper Award Session. (Canceled)},
}
[2]
Predict-and-recompute conjugate gradient variants.
Tyler Chen, Erin C. Carson.
Presentation at SIAM Parallel Processing.
@misc{predict_and_recompute_PP20,
    title = {Predict-and-recompute conjugate gradient variants},
    author={Tyler Chen and Erin C. Carson},
    author+an = {1=highlight},
    month = {February},
    year = {2020},
    note = {Presentation at SIAM Parallel Processing},
    url = {https://chen.pw/research/talks/predict_and_recompute_PP20.pdf}
}
[1]
Symmetric Preconditioner Refinement Using Low Rank Approximations.
Tyler Chen.
Presentation at Baidu Research.
@misc{symmetric_preconditioner_baidu,
    title = {Symmetric Preconditioner Refinement Using Low Rank Approximations},
    author = {Tyler Chen},
    year = {2019},
    note = {Presentation at Baidu Research},
}

Introductions to some topics I think are interesting

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.