2025 Submitted

A Hidden Variable Resultant Method for the Polynomial Multiparameter Eigenvalue Problem

E. Graf and A. Townsend

Submitted

eigenvalue problemsnumerical linear algebra

2025 Submitted

The Distributional Koopman Operator for Random Dynamical Systems

M. Oprea, A. Townsend, and Y. Yang

Submitted

dynamical systemsoperator learning

2024 Journal

A Mathematical Guide to Operator Learning

N. Boulle and A. Townsend

Handbook of Numerical Analysis, 2024

featured operator learningdeep learning

2024 Journal

Are sketch-and-precondition least squares solvers numerically stable?

M. Meier, Y. Nakatsukasa, A. Townsend, and M. Webb

To appear in SIAM Journal on Matrix Analysis and Applications

numerical linear algebrascientific computing

2024 Journal

Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems

M. J. Colbrook, Q. Li, R. V. Raut, and A. Townsend

To appear in Nonlinear Dynamics

dynamical systemsscientific computing

2024 Journal

Leveraging the Hankel norm approximation and block-AAA algorithms in reduced order modeling

A. Yu and A. Townsend

To appear in Linear Algebra and its Applications

approximationnumerical linear algebra

2024 Submitted

Expander graphs are globally synchronizing

P. Abdalla, A. S. Bandeira, M. Kassabov, V. Souza, S. H. Strogatz, and A. Townsend

Submitted to CPAM

dynamical systems

2024 Submitted

Avoiding discretization issues for nonlinear eigenvalue problems

M. J. Colbrook and A. Townsend

Submitted to SIAM Journal on Matrix Analysis and Applications

eigenvalue problemsspectral methods

Talk

2024 Submitted

Operator learning for hyperbolic partial differential equations

C. Wang and A. Townsend

Submitted to JMLR

operator learningdeep learning

2024 Submitted

ContHutch++: Stochastic trace estimation for implicit integral operators

J. Zvonek, A. Horning, and A. Townsend

Submitted to SINUM

numerical linear algebraoperator learning

2023 Journal

Elliptic PDE learning is provably data-efficient

N. Boulle, D. Halikias, and A. Townsend

PNAS, 2023

featured operator learningdeep learning

2023 Journal

Matrix recovery from matrix-vector products

D. Halikias and A. Townsend

Linear Algebra and its Applications, 2023

low-ranknumerical linear algebra

2023 Journal

The ResDMD paper

M. J. Colbrook and A. Townsend

Communications on Pure and Applied Mathematics, 2023

featured dynamical systemsoperator learning

2023 Journal

On the stability of unevenly spaced samples for interpolation and quadrature

A. Yu and A. Townsend

BIT Numerical Mathematics, 2023

approximationspectral methods

2023 Journal

A Quadrature Perspective on Frequency Bias in Neural Network Training with Nonuniform Data

A. Yu, Y. Yang, and A. Townsend

ICLR, 2023

deep learningapproximation

2023 Journal

Parallel algorithms for computing the tensor-train decomposition

T. Shi, M. Ruth, and A. Townsend

SIAM Journal on Scientific Computing, 2023

tensorslow-rank

2022 Journal

Exploring the electric field around a loop of static charge: Rectangles, stadiums, ellipses, and knots

M. Lipton, S. Strogatz, and A. Townsend

Physical Review Research, 2022

scientific computingdynamical systems

2022 Journal

Probabilistic Missing Value Imputation for Mixed Categorical and Ordered Data

Y. Zhao, A. Townsend, and M. Udell

NeurIPS, 2022

deep learninglow-rank

2022 Journal

Learning Green's functions associated with parabolic partial differential equations

N. Boulle, S. Kim, T. Shi, and A. Townsend

Journal of Machine Learning Research, 2022

operator learningdeep learning

Talk

2022 Journal

A global synchronization theorem for oscillators on a random graph

M. Kassabov, S. H. Strogatz, and A. Townsend

Chaos, 2022

dynamical systems

Talk

2022 Journal

Bounding Zolotarev numbers using Faber rational functions

D. Rubin, A. Townsend, and H. Wilber

Constructive Approximation, 2022

approximationnumerical linear algebra

Talk

2022 Journal

Data-driven discovery of Green's functions with human-understandable deep learning

N. Boulle, C. J. Earls, and A. Townsend

Proceedings volume, 2022

operator learningdeep learning

2022 Journal

A generalization of the randomized singular value decomposition

N. Boulle and A. Townsend

ICLR, 2022

low-ranknumerical linear algebra

2022 Journal

Data-driven Algorithms for signal processing with rational functions

H. Wilber, A. Damle, and A. Townsend

SIAM Journal on Scientific Computing, 2022

approximationscientific computing

2022 Journal

Learning elliptic partial differential equations with randomized linear algebra

N. Boulle and A. Townsend

Foundations of Computational Mathematics, 2022

operator learninglow-rank

2021 Journal

Suppression of electroconvective and morphological instabilities by an imposed cross flow of the electrolyte

G. Li, A. Townsend, L. A. Archer, and D. L. Koch

Physical Review Fluids, 2021

fluid dynamicsscientific computing

2021 Journal

Electroconvection and Electrodeposition on a Surface with Butler-Volmer Kinetics

G. Li, A. Townsend, L. A. Archer, and D. L. Koch

Journal of Fluid Mechanics, 2021

fluid dynamicsscientific computing

2021 Journal

Anderson acceleration using the H^{-s} norm

Y. Yang, A. Townsend, and D. Appelo

Journal of Computational and Applied Mathematics, 2021

scientific computingnumerical linear algebra

2021 Journal

Sufficiently dense Kuramoto networks are globally synchronizing

M. Kassabov, S. H. Strogatz, and A. Townsend

Chaos, 2021

dynamical systems

2021 Journal

Computing spectral measures of self-adjoint operators

M. J. Colbrook, A. Horning, and A. Townsend

SIAM Review, 2021

eigenvalue problemsspectral methods

Talk

2021 Journal

The ultraspherical spectral element method

D. Fortunato, N. Hale, and A. Townsend

Journal of Computational Physics, 2021

spectral methodsscientific computing

Talk

2021 Journal

On the compressibility of tensors

T. Shi and A. Townsend

SIAM Journal on Matrix Analysis and Applications, 2021

tensorslow-rank

2020 Journal

Rational neural networks

N. Boulle, Y. Nakatsukasa, and A. Townsend

NeurIPS, 2020

featured deep learningapproximation

2020 Journal

Error localization of best L1 polynomial approximants

Y. Nakatsukasa and A. Townsend

SIAM Journal on Numerical Analysis, 2020

approximation

2020 Journal

Dense networks that do not synchronize and sparse ones that do

A. Townsend, M. Stillman, and S. H. Strogatz

Chaos, 2020

dynamical systems

2020 Journal

Computing with functions on the ball

N. Boulle and A. Townsend

SIAM Journal on Scientific Computing, 2020

spectral methodsscientific computing

2020 Journal

FEAST for differential eigenvalue problems

A. Horning and A. Townsend

SIAM Journal on Numerical Analysis, 2020

eigenvalue problemsnumerical linear algebra

2020 Journal

Recurrence relations for a family of orthogonal polynomials on a triangle

S. Olver, A. Townsend, and G. M. Vasil

ICOSAHOM Proceedings, 2020

approximationspectral methods

2020 Journal

Fast Poisson solvers for spectral methods

D. Fortunato and A. Townsend

IMA Journal of Numerical Analysis, 2020

spectral methodsscientific computing

2019 Journal

A sparse spectral method on triangles

S. Olver, A. Townsend, and G. Vasil

SIAM Journal on Scientific Computing, 2019

spectral methodsscientific computing

2019 Journal

Chebyshev approximation and the global geometry of sloppy models

K. N. Quinn, H. Wilber, A. Townsend, and J. P. Sethna

Physical Review Letters, 2019

approximationscientific computing

2019 Journal

Continuous analogues of Krylov methods for differential operators

M. A. Gilles and A. Townsend

SIAM Journal on Numerical Analysis, 2019

numerical linear algebraspectral methods

2019 Journal

Bounds on the singular values of matrices with displacement structure

B. Beckermann and A. Townsend

SIAM Review, 2019

low-ranknumerical linear algebra

2019 Journal

Why are big data matrices approximately of low rank?

M. Udell and A. Townsend

SIAM Journal on Mathematics of Data Science, 2019

featured low-rankdata science

Talk

2018 Journal

Stokes' second problem and an Einstein-de Haas analogue effect in active fluids

J. Slomka, A. Townsend, and J. Dunkel

Physical Review Fluids, 2018

fluid dynamicsdynamical systems

2018 Journal

On the singular values of matrices with high displacement rank

A. Townsend and H. Wilber

Linear Algebra and its Applications, 2018

low-ranknumerical linear algebra

2018 Journal

A nonuniform fast Fourier transform based on low rank approximation

D. Antolin-Ruiz and A. Townsend

SIAM Journal on Scientific Computing, 2018

low-rankspectral methods

2018 Journal

Fast polynomial transforms based on Toeplitz and Hankel matrices

A. Townsend, M. Webb, and S. Olver

Mathematics of Computation, 2018

spectral methodsapproximation

Talk

2017 Journal

On the singular values of matrices with displacement structure

B. Beckermann and A. Townsend

SIAM Journal on Matrix Analysis and Applications, 2017

low-ranknumerical linear algebra

2017 Journal

Computing with functions in spherical and polar geometries II. The disk

A. Townsend, H. Wilber, and G. B. Wright

SIAM Journal on Scientific Computing, 2017

spectral methodsscientific computing

2016 Journal

Stable extrapolation of analytic functions

L. Demanet and A. Townsend

Foundations of Computational Mathematics, 2016

approximation

2016 Journal

Vector spaces of linearizations for matrix polynomials: A bivariate polynomial approach

V. Noferini, Y. Nakatsukasa, and A. Townsend

SIAM Journal on Matrix Analysis and Applications, 2016

eigenvalue problemsnumerical linear algebra

2016 Journal

A fast FFT-based discrete Legendre transform

N. Hale and A. Townsend

IMA Journal of Numerical Analysis, 2016

spectral methodsapproximation

2016 Journal

Computing with functions in spherical and polar geometries I. The sphere

A. Townsend, H. Wilber, and G. B. Wright

SIAM Journal on Scientific Computing, 2016

spectral methodsscientific computing

2016 Journal

Numerical instability of resultant methods for multidimensional rootfinding

V. Noferini and A. Townsend

SIAM Journal on Numerical Analysis, 2016

scientific computingnumerical linear algebra

2016 Journal

Fast computation of Gauss quadrature nodes and weights on the whole real line

A. Townsend, T. Trogdon, and S. Olver

IMA Journal of Numerical Analysis, 2016

approximationspectral methods

2015 Journal

The automatic solution of partial differential equations using a global spectral method

A. Townsend and S. Olver

Journal of Computational Physics, 2015

spectral methodsscientific computing

2015 Journal

A fast analysis-based discrete Hankel transform using asymptotic formulas

A. Townsend

SIAM Journal on Numerical Analysis, 2015

spectral methodsapproximation

Talk

2015 Journal

Computing the common zeros of two bivariate functions via Bezout resultants

Y. Nakatsukasa, V. Noferini, and A. Townsend

Numerische Mathematik, 2015

numerical linear algebrascientific computing

2015 Journal

Continuous analogues of matrix factorizations

A. Townsend and L. N. Trefethen

Proceedings of the Royal Society A, 2015

numerical linear algebraspectral methods

2014 Journal

An algorithm for the convolution of Legendre series

N. Hale and A. Townsend

SIAM Journal on Scientific Computing, 2014

spectral methodsapproximation

2014 Journal

A fast, simple, and stable Chebyshev-Legendre transform using an asymptotic formula

N. Hale and A. Townsend

SIAM Journal on Scientific Computing, 2014

spectral methodsapproximation

2013 Journal

An extension of Chebfun to two dimensions

A. Townsend and L. N. Trefethen

SIAM Journal on Scientific Computing, 2013

spectral methodsscientific computing

2013 Journal

Fast and accurate computation of Gauss-Legendre and Gauss-Jacobi quadrature nodes and weights

N. Hale and A. Townsend

SIAM Journal on Scientific Computing, 2013

approximationspectral methods

2013 Journal

A fast and well-conditioned spectral method

S. Olver and A. Townsend

SIAM Review, 2013

featured spectral methodsscientific computing

Talk

2013 Journal

Multiscale analysis in Sobolev spaces on bounded domains with zero boundary values

A. Townsend and H. Wendland

IMA Journal of Numerical Analysis, 2013

scientific computingapproximation