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 numerical analysis, theoretical computer science, and applied computational sciences such as quantum physics.

I am committed to making my research accessible and to facilitating the reproducibility/replicability of my work. Code to generate the figures from my papers can be found on Github. Please feel free to contact me with any questions or concerns about my research.

In the fall I will be starting as a Courant Instructor, sponsored by Chris Musco.

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!

Thesis

Lanczos based methods for matrix functions (coming soon!)

I was advised by Anne Greenbaum and Tom Trogdon.

Publications

More information can be found in my CV. In general, I’ve tried to include brief 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.

[9]
On the fast convergence of minibatch heavy ball momentum

Raghu Bollapragada, Tyler Chen, Rachel Ward

@misc{minibatch_HBM,
    title={On the fast convergence of minibatch heavy ball momentum},
    author={Raghu Bollapragada and Tyler Chen and Rachel Ward},
    year={2022},
    eprint={2206.07553},
    archivePrefix={arXiv},
    primaryClass={cs.LG}
}
[8]
Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems

Tyler Chen, Yu-Chen Cheng

@misc{reduced_density,
    title={Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems},
    author={Tyler Chen and Yu-Chen Cheng},
    year={2022},
    eprint={2204.08147},
    archivePrefix={arXiv},
    primaryClass={quant-ph}
}
[7]
Randomized matrix-free quadrature for spectrum, spectral sum approximation

Tyler Chen, Thomas Trogdon, Shashanka Ubaru

@misc{matrix_free_quadrature,
    title={Randomized matrix-free quadrature for spectrum and spectral sum approximation},
    author={Tyler Chen and Thomas Trogdon and Shashanka Ubaru},
    author+an = {1=highlight},
    year={2022},
    eprint={2204.01941},
    archivePrefix={arXiv},
    primaryClass={math.NA}
}
[6]
Low-memory Krylov subspace methods for optimal rational matrix function approximation

Tyler Chen, Anne Greenbaum, Cameron Musco, Christopher Musco

@misc{lowmem_rational_opt,
    title={Low-memory Krylov subspace methods for optimal rational matrix function approximation},
    author={Tyler Chen and Anne Greenbaum and Cameron Musco and Christopher Musco},
    year={2022},
    eprint={2202.11251},
    archivePrefix={arXiv},
    primaryClass={math.NA},
}
[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,
    doi = {10.1137/21m1427784},
    url = {https://doi.org/10.1137/21m1427784},
    year = {2022},
    month = may,
    publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
    volume = {43},
    number = {2},
    pages = {787--811},
    author = {Tyler Chen and Anne Greenbaum and Cameron Musco and Christopher Musco},
    title = {Error Bounds for Lanczos-Based Matrix Function Approximation},
    journal = {SIAM Journal on Matrix Analysis and Applications},
    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.

Introductions to some topics I think are interesting