Research
I am a Courant Instructor at New York University, sponsored by Christopher Musco.
I have a joint appoinment with Mathematics at Courant and Computer Science and Engineering at Tandon.
Broadly, my research aims to develop methods to support the scientists taking on the problems of today.
I’m particularly 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 mainly 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.
More information can be found in my 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.
- Robert Chen (NYU)
- Kevin Li (NYU)
- Skai Nzeuton (Stuyvesant)
- Yilu Pan (NYU)
- Yixin Wang (NYU)
- Qichen Xu (UW)
If you’re an undergrad student in the NYC area interested in research or grad school, please feel free to reach out.
In submission
[7]
GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginibre matrices
Tyler Chen, Anne Greenbaum, and Thomas Trogdon.
2023
.
[6]
Stability of the Lanczos algorithm on matrices with regular spectral distributions
Tyler Chen and Thomas Trogdon.
2023
.
[5]
Near-Optimality Guarantees for Approximating Rational Matrix Functions by the Lanczos Method
Noah Amsel, Tyler Chen, Anne Greenbaum, Cameron Musco, and Chris Musco.
2023
.
[4]
A posteriori error bounds for the block-Lanczos method for matrix function approximation
Qichen Xu and Tyler Chen.
2022
.
[3]
On the fast convergence of minibatch heavy ball momentum
Raghu Bollapragada, Tyler Chen, and Rachel Ward.
2022
.
[2]
Krylov-aware stochastic trace estimation
Tyler Chen and Eric Hallman.
2022
.
[1]
Randomized matrix-free quadrature for spectrum and spectral sum approximation
Tyler Chen, Thomas Trogdon, and Shashanka Ubaru.
2022
.
Publications
[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
.
to appear
[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 where I was advised by Anne Greenbaum and Tom Trogdon.
Lanczos based methods for matrix functions
[PDF]
[source]
[commentary on design]
Talks
[11]
Randomized matrix-free qudrature
2022
.
Presentation at Courant Numerical Analysis and Scientific Computing Seminar
[10]
GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginbre matrices
Presentation at Conference on Random Matrix Theory and Numerical Linear Algebra.
2022
.
[10]
GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginbre matrices
Presentation at Conference on Random Matrix Theory and Numerical Linear Algebra.
2022
.
[8]
Simple Algorithms for Spectral Sum and Spectrum Approximation
Poster at Workshop on Algorithms for Large Data (Online).
2021
.
[7]
Analysis of stochastic Lanczos quadrature for spectrum approximation
Oral at International Conference on Machine Learning.
2021
.
[6]
Concentration in the Lanczos Algorithm
Presentation at SIAM Linear Algebra 21.
2021
.
[5]
Analysis of stochastic Lanczos quadrature for spectrum approximation
Presentation at at Baidu Research.
2021
.
[4]
Analyzing the Effects of Local Roundoff Error on Predict-and-Recompute Conjugate Gradient Variants
Poster at Householder Symposium (Cancelled).
2020
.
[3]
Predict-and-recompute conjugate gradient variants
Presentation at Copper Mountain Student Paper Award Session (Cancelled).
2020
.
[2]
Predict-and-recompute conjugate gradient variants
Presentation at SIAM Parallel Processing.
2020
.
[1]
Symmetric Preconditioner Refinement Using Low Rank Approximations
Presentation at Baidu Research.
2019
.