Publications

Selected papers are highlighted first, followed by a compact chronological list with direct links to arXiv versions and published versions where available.

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Selected Publications

Complete List

All Publications

A compact chronological list of journal papers, conference papers, and preprints. Also see my Google Scholar and CV.

  1. 2026

    Oblivious Subspace Injection Is Not Enough for Relative Error

    A. Townsend and C. Wang

    arXiv preprint, 2026

    ArXiv
  2. 2026

    Beyond singular value gaps in randomized subspace approximation

    C. Wang and A. Townsend

    arXiv preprint, 2026

    ArXiv
  3. 2026

    Rational Neural Networks have Expressivity Advantages

    M. Tang and A. Townsend

    arXiv preprint, 2026

    ArXiv
  4. 2026

    Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop

    N. Amsel, Y. Baumann, P. Beckman, P. Burgisser, C. Camano, T. Chen, et al.

    arXiv preprint, 2026

    ArXiv
  5. 2026

    Estimating a matrix's singular values with interpolative decompositions

    A. Damle, S. Glas, A. Townsend, and A. Yu

    Linear Algebra and its Applications 731, 306-342, 2026

    ArXivPublished
  6. 2026

    Numerical instability of algebraic rootfinders

    E. Graf and A. Townsend

    Linear Algebra and its Applications 729, 308-336, 2026

    ArXivPublished
  7. 2026

    Expander graphs are globally synchronizing

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

    Advances in Mathematics 488, 110773, 2026

    ArXivPublished
  8. 2025

    Convergence of Pivoted Cholesky Algorithm for Lipschitz Kernels

    S. Jeong and A. Townsend

    arXiv preprint, 2025

    ArXiv
  9. 2025

    Extending Mercer's expansion to indefinite and asymmetric kernels

    S. Jeong and A. Townsend

    ICLR, 2025

    ArXivPublished
  10. 2025

    A hidden variable resultant method for the polynomial multiparameter eigenvalue problem

    E. Graf and A. Townsend

    Linear Algebra and its Applications 727, 37-60, 2025

    ArXivPublished
  11. 2025

    The distributional Koopman operator for random dynamical systems

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

    Mathematics of Control, Signals, and Systems 37(4), 769-798, 2025

    ArXivPublished
  12. 2025

    Avoiding Discretization Issues for Nonlinear Eigenvalue Problems

    M. J. Colbrook and A. Townsend

    SIAM Journal on Matrix Analysis and Applications 46(1), 648-675, 2025

    ArXivPublishedTalk
  13. 2025

    Operator Learning for Hyperbolic Partial Differential Equations

    C. Wang and A. Townsend

    Journal of Machine Learning Research 26(199), 1-44, 2025

    ArXivPublished
  14. 2025

    ContHutch++: Stochastic Trace Estimation for Implicit Integral Operators

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

    SIAM Journal on Numerical Analysis 63(1), 334-359, 2025

    ArXivPublished
  15. 2024

    Operator learning without the adjoint

    N. Boulle, D. Halikias, S. E. Otto, and A. Townsend

    Journal of Machine Learning Research 25(364), 1-54, 2024

    ArXivPublished
  16. 2024

    A Mathematical Guide to Operator Learning

    N. Boulle and A. Townsend

    Handbook of Numerical Analysis 25, 83-125, 2024

    ArXivPublished
  17. 2024

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

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

    SIAM Journal on Matrix Analysis and Applications 45(2), 905-929, 2024

    ArXivPublished
  18. 2024

    Beyond expectations: Residual Dynamic Mode Decomposition and variance for stochastic dynamical systems

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

    Nonlinear Dynamics 112(3), 2037-2061, 2024

    ArXivPublished
  19. 2024

    Leveraging the Hankel norm approximation and data-driven algorithms in reduced order modeling

    A. Yu and A. Townsend

    Numerical Linear Algebra with Applications 31(4), e2555, 2024

    ArXivPublished
  20. 2024

    Structured matrix recovery from matrix-vector products

    D. Halikias and A. Townsend

    Numerical Linear Algebra with Applications 31(1), e2531, 2024

    ArXivPublished
  21. 2024

    Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems

    M. J. Colbrook and A. Townsend

    Communications on Pure and Applied Mathematics 77(1), 221-283, 2024

    ArXivPublished
  22. 2023

    Elliptic PDE learning is provably data-efficient

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

    PNAS, 2023

    ArXiv
  23. 2023

    On the stability of unevenly spaced samples for interpolation and quadrature

    A. Yu and A. Townsend

    BIT Numerical Mathematics, 2023

    ArXiv
  24. 2023

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

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

    ICLR, 2023

    ArXiv
  25. 2023

    Parallel algorithms for computing the tensor-train decomposition

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

    SIAM Journal on Scientific Computing, 2023

    ArXiv
  26. 2022

    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

    ArXiv
  27. 2022

    Probabilistic Missing Value Imputation for Mixed Categorical and Ordered Data

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

    NeurIPS, 2022

    Published
  28. 2022

    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

    ArXivTalk
  29. 2022

    A global synchronization theorem for oscillators on a random graph

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

    Chaos, 2022

    ArXivTalk
  30. 2022

    Bounding Zolotarev numbers using Faber rational functions

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

    Constructive Approximation, 2022

    ArXivTalk
  31. 2022

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

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

    Proceedings volume, 2022

    ArXiv
  32. 2022

    A generalization of the randomized singular value decomposition

    N. Boulle and A. Townsend

    ICLR, 2022

    ArXiv
  33. 2022

    Data-driven Algorithms for signal processing with rational functions

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

    SIAM Journal on Scientific Computing, 2022

    ArXiv
  34. 2022

    Learning elliptic partial differential equations with randomized linear algebra

    N. Boulle and A. Townsend

    Foundations of Computational Mathematics, 2022

    Published
  35. 2021

    Arbitrary-depth universal approximation theorems for operator neural networks

    A. Yu, C. Becquey, D. Halikias, M. E. Mallory, and A. Townsend

    arXiv preprint, 2021

    ArXiv
  36. 2021

    An optimal complexity spectral method for Navier--Stokes simulations in the ball

    N. Boulle, J. Slomka, and A. Townsend

    arXiv preprint, 2021

    ArXiv
  37. 2021

    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

    Published
  38. 2021

    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

    Published
  39. 2021

    Anderson acceleration using the H^{-s} norm

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

    Journal of Computational and Applied Mathematics, 2021

    ArXiv
  40. 2021

    Sufficiently dense Kuramoto networks are globally synchronizing

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

    Chaos, 2021

    Published
  41. 2021

    Computing spectral measures of self-adjoint operators

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

    SIAM Review, 2021

    ArXivTalk
  42. 2021

    The ultraspherical spectral element method

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

    Journal of Computational Physics, 2021

    PublishedTalk
  43. 2021

    On the compressibility of tensors

    T. Shi and A. Townsend

    SIAM Journal on Matrix Analysis and Applications, 2021

    Published
  44. 2020

    Fast algorithms using orthogonal polynomials

    S. Olver, R. M. Slevinsky, and A. Townsend

    Acta Numerica 29, 573-699, 2020

    Published
  45. 2020

    Over-parametrized neural networks as under-determined linear systems

    A. R. Benson, A. Damle, and A. Townsend

    arXiv preprint, 2020

    ArXiv
  46. 2020

    Rational neural networks

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

    NeurIPS, 2020

    ArXiv
  47. 2020

    Error localization of best L1 polynomial approximants

    Y. Nakatsukasa and A. Townsend

    SIAM Journal on Numerical Analysis, 2020

    Published
  48. 2020

    Dense networks that do not synchronize and sparse ones that do

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

    Chaos, 2020

    Published
  49. 2020

    Computing with functions on the ball

    N. Boulle and A. Townsend

    SIAM Journal on Scientific Computing, 2020

    Published
  50. 2020

    FEAST for differential eigenvalue problems

    A. Horning and A. Townsend

    SIAM Journal on Numerical Analysis, 2020

    Published
  51. 2020

    Recurrence relations for a family of orthogonal polynomials on a triangle

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

    ICOSAHOM Proceedings, 2020

    ArXiv
  52. 2020

    Fast Poisson solvers for spectral methods

    D. Fortunato and A. Townsend

    IMA Journal of Numerical Analysis, 2020

    Published
  53. 2019

    A sparse spectral method on triangles

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

    SIAM Journal on Scientific Computing, 2019

    Published
  54. 2019

    Chebyshev approximation and the global geometry of sloppy models

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

    Physical Review Letters, 2019

    Published
  55. 2019

    Continuous analogues of Krylov methods for differential operators

    M. A. Gilles and A. Townsend

    SIAM Journal on Numerical Analysis, 2019

    Published
  56. 2019

    Bounds on the singular values of matrices with displacement structure

    B. Beckermann and A. Townsend

    SIAM Review, 2019

    Published
  57. 2019

    Why are big data matrices approximately of low rank?

    M. Udell and A. Townsend

    SIAM Journal on Mathematics of Data Science, 2019

    PublishedTalk
  58. 2018

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

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

    Physical Review Fluids, 2018

    Published
  59. 2018

    On the singular values of matrices with high displacement rank

    A. Townsend and H. Wilber

    Linear Algebra and its Applications, 2018

    Published
  60. 2018

    A nonuniform fast Fourier transform based on low rank approximation

    D. Antolin-Ruiz and A. Townsend

    SIAM Journal on Scientific Computing, 2018

    Published
  61. 2018

    Fast polynomial transforms based on Toeplitz and Hankel matrices

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

    Mathematics of Computation, 2018

    PublishedTalk
  62. 2017

    On the singular values of matrices with displacement structure

    B. Beckermann and A. Townsend

    SIAM Journal on Matrix Analysis and Applications, 2017

    Published
  63. 2017

    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

    Published
  64. 2016

    Stable extrapolation of analytic functions

    L. Demanet and A. Townsend

    Foundations of Computational Mathematics, 2016

    Published
  65. 2016

    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

    Published
  66. 2016

    A fast FFT-based discrete Legendre transform

    N. Hale and A. Townsend

    IMA Journal of Numerical Analysis, 2016

    Published
  67. 2016

    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

    Published
  68. 2016

    Numerical instability of resultant methods for multidimensional rootfinding

    V. Noferini and A. Townsend

    SIAM Journal on Numerical Analysis, 2016

    Published
  69. 2016

    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

    Published
  70. 2015

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

    A. Townsend and S. Olver

    Journal of Computational Physics, 2015

    Published
  71. 2015

    A fast analysis-based discrete Hankel transform using asymptotic formulas

    A. Townsend

    SIAM Journal on Numerical Analysis, 2015

    PublishedTalk
  72. 2015

    Computing the common zeros of two bivariate functions via Bezout resultants

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

    Numerische Mathematik, 2015

    Published
  73. 2015

    Continuous analogues of matrix factorizations

    A. Townsend and L. N. Trefethen

    Proceedings of the Royal Society A, 2015

    Published
  74. 2014

    A practical framework for infinite-dimensional linear algebra

    S. Olver and A. Townsend

    HPTCDL, 2014

    Published
  75. 2014

    An algorithm for the convolution of Legendre series

    N. Hale and A. Townsend

    SIAM Journal on Scientific Computing, 2014

    Published
  76. 2014

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

    N. Hale and A. Townsend

    SIAM Journal on Scientific Computing, 2014

    Published
  77. 2013

    Fast inverse transform sampling in one and two dimensions

    S. Olver and A. Townsend

    arXiv preprint, 2013

    ArXiv
  78. 2013

    An extension of Chebfun to two dimensions

    A. Townsend and L. N. Trefethen

    SIAM Journal on Scientific Computing, 2013

    Published
  79. 2013

    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

    Published
  80. 2013

    A fast and well-conditioned spectral method

    S. Olver and A. Townsend

    SIAM Review, 2013

    PublishedTalk
  81. 2013

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

    A. Townsend and H. Wendland

    IMA Journal of Numerical Analysis, 2013

    Published