Tyler Chen

I am an Assistant Professor / Courant Instructor at New York University, with a joint appoinment with Mathematics at Courant and Computer Science and Engineering at Tandon. My position is sponsored by Christopher Musco. I got my PhD in Applied Math from the University of Washington, where I was advised by Anne Greenbaum and Tom Trogdon. Before that, I was an Math and Physics student at Tufts University.

Broadly, my research aims to develop methods to support the scientists taking on the problems of today by providing fast (in theory and practice) algorithms for core linear algebra tasks. An overview of my research interests along with more detailed introductions to particular directions can be found here as well as by following the links on papers listed below.

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.

Materials from my past applications and proposals can be found here.

Key Info

tyler.chen@nyu.edu

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WWH 920

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370 Jay St. 1110

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curriculum vitae (cv)

Collaboration

I’m always interested in finding things to collaborate on (and people to collaborate with). I’m especially interested in cross-disciplinary work.

I believe strongly in the value of undergraduate research and am currently working with a number of undergraduate students on research projects.

If you’re an undergrad student in the NYC area interested in research or grad school, please feel free to reach out. While I don’t currently have any research positions, I’m happy to discuss these things with you.

Talks

Slides for my talks and a list of upcoming travel can be found here.

Papers (in progress)

[8]
Randomized block Krylov subspace methods for low rank approximation of matrix functions

David Persson, Tyler Chen, and Christopher Musco.
2024
.
[7]
Fixed-sparsity matrix approximation from matrix-vector products

Noah Amsel, Tyler Chen, Feyza Duman Keles, Diana Halikias, Cameron Musco, and Christopher Musco.
2024
.
[6]
Faster randomized partial trace estimation

Tyler Chen, Robert Chen, Kevin Li, Skai Nzeuton, Yilu Pan, and Yixin Wang.
2023
.
[5]
Optimal Polynomial Approximation to Rational Matrix Functions Using the Arnoldi Algorithm

Tyler Chen, Anne Greenbaum, and Natalie Wellen.
2023
.
[4]
Near-Optimality Guarantees for Approximating Rational Matrix Functions by the Lanczos Method

Noah Amsel, Tyler Chen, Anne Greenbaum, Cameron Musco, and Christopher Musco.
2023
.
[3]
A posteriori error bounds for the block-Lanczos method for matrix function approximation

Qichen Xu and Tyler Chen.
2022
.
[2]
On the fast convergence of minibatch heavy ball momentum

Raghu Bollapragada, Tyler Chen, and Rachel Ward.
2022
.
[1]
Randomized matrix-free quadrature for spectrum and spectral sum approximation

Tyler Chen, Thomas Trogdon, and Shashanka Ubaru.
2022
.

Papers (published)

[11]
GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginibre matrices

Tyler Chen, Anne Greenbaum, and Thomas Trogdon.
Mathematics of Computation.
2024
.
To appear
[10]
Stability of the Lanczos algorithm on matrices with regular spectral distributions

Chen, Tyler and Trogdon, Thomas.
Linear Algebra and its Applications.
2024
.
[9]
A spectrum adaptive kernel polynomial method

Tyler Chen.
The Journal of Chemical Physics.
2023
.
[8]
Krylov-Aware Stochastic Trace Estimation

Tyler Chen and Eric Hallman.
SIAM Journal on Matrix Analysis and Applications.
2023
.
[7]
Low-Memory Krylov Subspace Methods for Optimal Rational Matrix Function Approximation

Tyler Chen, Anne Greenbaum, Cameron Musco, and Christopher Musco.
SIAM Journal on Matrix Analysis and Applications.
2023
.
[6]
Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems

Tyler Chen and Yu-Chen Cheng.
The Journal of Chemical Physics.
2022
.
[5]
Error Bounds for Lanczos-Based Matrix Function Approximation

Tyler Chen, Anne Greenbaum, Cameron Musco, and Christopher Musco.
SIAM Journal on Matrix Analysis and Applications.
2022
.
[4]
Analysis of stochastic Lanczos quadrature for spectrum approximation

Tyler Chen, Thomas Trogdon, and Shashanka Ubaru.
Proceedings of the 38th International Conference on Machine Learning.
2021
.
[3]
On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic

Anne Greenbaum, Hexuan Liu, and Tyler Chen.
SIAM Journal on Scientific Computing.
2021
.
[2]
Non-asymptotic moment bounds for random variables rounded to non-uniformly spaced sets

Tyler Chen.
Stat.
2021
.
[1]
Predict-and-recompute conjugate gradient variants

Tyler Chen and Erin C. Carson.
SIAM Journal on Scientific Computing.
2020
.

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

Thesis

I did my PhD in the Department of Applied Mathematics at the University of Washington. I was advised by Anne Greenbaum and Tom Trogdon.

Lanczos based methods for matrix functions
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