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).

If you’re an undergrad student in the NYC area 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

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]

In submission

[4]
On the fast convergence of minibatch heavy ball momentum

Raghu Bollapragada, Tyler Chen, and Rachel Ward

[3]
Krylov-aware stochastic trace estimation

Tyler Chen and Eric Hallman

[2]
Randomized matrix-free quadrature for spectrum and spectral sum approximation

Tyler Chen, Thomas Trogdon, and Shashanka Ubaru

[1]
Low-memory Krylov subspace methods for optimal rational matrix function approximation

Tyler Chen, Anne Greenbaum, Cameron Musco, and Christopher Musco

Publications

[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

[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

[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

[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

[2]
Non-asymptotic moment bounds for random variables rounded to non-uniformly spaced sets

Tyler Chen

Stat

[1]
Predict-and-recompute conjugate gradient variants

Tyler Chen and Erin C. Carson

SIAM Journal on Scientific Computing

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

Talks

[9]
GMRES, pseudospectra, and Crouzeix's conjecture for shifted and scaled Ginbre matrices

Presentation at Conference on Random Matrix Theory and Numerical Linear Algebra.

[8]
Simple Algorithms for Spectral Sum and Spectrum Approximation

Poster at Workshop on Algorithms for Large Data (Online).

[7]
Analysis of stochastic Lanczos quadrature for spectrum approximation

Oral at International Conference on Machine Learning.

[6]
Concentration in the Lanczos Algorithm

Presentation at SIAM Linear Algebra 21.

[5]
Analysis of stochastic Lanczos quadrature for spectrum approximation

Presentation at at Baidu Research.

[4]
Analyzing the Effects of Local Roundoff Error on Predict-and-Recompute Conjugate Gradient Variants

Poster at Householder Symposium (Cancelled).

[3]
Predict-and-recompute conjugate gradient variants

Presentation at Copper Mountain Student Paper Award Session (Cancelled).

[2]
Predict-and-recompute conjugate gradient variants

Presentation at SIAM Parallel Processing.

[1]
Symmetric Preconditioner Refinement Using Low Rank Approximations

Presentation at Baidu Research.