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. I work most closely with Chris 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 studied math, physics, and studio art at Tufts University.

Broadly, my research aims design and analyze 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’m always interested in finding things to collaborate on (and people to collaborate with).

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 about my research.

I am happy with “they” or “he” as pronouns.

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)

Student mentorship

I believe strongly in the value of undergraduate research and student mentorship, and am currently working with a several of undergraduate students on research projects. Previous projects with undergrads have resulted in publications. I am particularly committed to supporting students from groups underrepresented in math and students receiving federal work study or other need-based financial aid.

If you’re an undergrad student interested in research or grad school, please feel free to reach out; I’m always happy to answer quetions.

Talks

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

Papers (in progress)

[7]
Randomized block Krylov subspace methods for low rank approximation of matrix functions

David Persson, Tyler Chen, and Christopher Musco.
2024
.
[6]
Near-optimal convergence of the full orthogonalization method

Tyler Chen and Gérard Meurant.
2024
.
[5]
Fixed-sparsity matrix approximation from matrix-vector products

Noah Amsel, Tyler Chen, Feyza Duman Keles, Diana Halikias, Cameron Musco, and Christopher Musco.
2024
.
[4]
Faster randomized partial trace estimation

Tyler Chen, Robert Chen, Kevin Li, Skai Nzeuton, Yilu Pan, and Yixin Wang.
2023
.
[3]
Optimal Polynomial Approximation to Rational Matrix Functions Using the Arnoldi Algorithm

Tyler Chen, Anne Greenbaum, and Natalie Wellen.
2023
.
[2]
Near-Optimality Guarantees for Approximating Rational Matrix Functions by the Lanczos Method

Noah Amsel, Tyler Chen, Anne Greenbaum, Cameron Musco, and Christopher Musco.
2023
.

[1]
Randomized matrix-free quadrature for spectrum and spectral sum approximation

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

Papers (published)

[13]
On the fast convergence of minibatch heavy ball momentum

Raghu Bollapragada, Tyler Chen, and Rachel Ward.
IMA Journal of Numerical Analysis.
2024
.
To appear
[12]
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
[11]
A posteriori error bounds for the block-Lanczos method for matrix function approximation

Qichen Xu and Tyler Chen.
Numerical Algorithms.
2024
.
[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
.

Thesis

Lanczos based methods for matrix functions
[PDF] [source] [commentary on design]

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

Other

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