Alex Townsend

Publication Activity (10 Years)

Years Active: 2013-2024
Publications (10 Years): 63

Top Topics

Singular Values

Partial Differential Equations

Top Venues

SIAM J. Sci. Comput.

SIAM J. Numer. Anal.

SIAM J. Matrix Anal. Appl.

Publications

Maike Meier, Yuji Nakatsukasa, Alex Townsend, Marcus Webb
Are Sketch-and-Precondition Least Squares Solvers Numerically Stable? SIAM J. Matrix Anal. Appl. 45 (2) (2024)
Anil Damle, Silke Glas, Alex Townsend, Annan Yu
How to reveal the rank of a matrix? CoRR (2024)
Diana Halikias, Alex Townsend
Structured matrix recovery from matrix-vector products. Numer. Linear Algebra Appl. 31 (1) (2024)
Nicolas Boullé, Diana Halikias, Samuel E. Otto, Alex Townsend
Operator learning without the adjoint. CoRR (2024)
Annan Yu, Alex Townsend
Leveraging the Hankel norm approximation and data-driven algorithms in reduced order modeling. Numer. Linear Algebra Appl. 31 (4) (2024)
Matthew J. Colbrook, Qin Li, Ryan V. Raut, Alex Townsend
Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems. CoRR (2023)
Annan Yu, Alex Townsend
Leveraging the Hankel norm approximation and block-AAA algorithms in reduced order modeling. CoRR (2023)
Nicolas Boullé, Alex Townsend
Learning Elliptic Partial Differential Equations with Randomized Linear Algebra. Found. Comput. Math. 23 (2) (2023)
Christopher Wang, Alex Townsend
Operator learning for hyperbolic partial differential equations. CoRR (2023)
Tianyi Shi, Maximilian Ruth, Alex Townsend
Parallel Algorithms for Computing the Tensor-Train Decomposition. SIAM J. Sci. Comput. 45 (3) (2023)
Nicolas Boullé, Diana Halikias, Alex Townsend
Elliptic PDE learning is provably data-efficient. CoRR (2023)
Matthew J. Colbrook, Alex Townsend
Avoiding discretization issues for nonlinear eigenvalue problems. CoRR (2023)
Maike Meier, Yuji Nakatsukasa, Alex Townsend, Marcus Webb
Are sketch-and-precondition least squares solvers numerically stable? CoRR (2023)
Jennifer Zvonek, Andrew Horning, Alex Townsend
ContHutch++: Stochastic trace estimation for implicit integral operators. CoRR (2023)
Nicolas Boullé, Alex Townsend
A Mathematical Guide to Operator Learning. CoRR (2023)
Annan Yu, Yunan Yang, Alex Townsend
Tuning Frequency Bias in Neural Network Training with Nonuniform Data. ICLR (2023)
Diana Halikias, Alex Townsend
Matrix recovery from matrix-vector products. CoRR (2022)
Annan Yu, Yunan Yang, Alex Townsend
A Quadrature Perspective on Frequency Bias in Neural Network Training with Nonuniform Data. CoRR (2022)
Yuxuan Zhao, Alex Townsend, Madeleine Udell
Probabilistic Missing Value Imputation for Mixed Categorical and Ordered Data. NeurIPS (2022)
Annan Yu, Alex Townsend
On the stability of unevenly spaced samples for interpolation and quadrature. CoRR (2022)
Nicolas Boullé, Seick Kim, Tianyi Shi, Alex Townsend
Learning Green's functions associated with parabolic partial differential equations. CoRR (2022)
Heather Wilber, Anil Damle, Alex Townsend
Data-Driven Algorithms for Signal Processing with Trigonometric Rational Functions. SIAM J. Sci. Comput. 44 (3) (2022)
Nicolas Boullé, Alex Townsend
A generalization of the randomized singular value decomposition. ICLR (2022)
Nicolas Boullé, Seick Kim, Tianyi Shi, Alex Townsend
Learning Green's functions associated with time-dependent partial differential equations. J. Mach. Learn. Res. 23 (2022)
Yunan Yang, Alex Townsend, Daniel Appelö
Anderson acceleration based on the H-s Sobolev norm for contractive and noncontractive fixed-point operators. J. Comput. Appl. Math. 403 (2022)
Annan Yu, Chloé Becquey, Diana Halikias, Matthew Esmaili Mallory, Alex Townsend
Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks. CoRR (2021)
Nicolas Boullé, Jonasz Slomka, Alex Townsend
An optimal complexity spectral method for Navier-Stokes simulations in the ball. CoRR (2021)
Nicolas Boullé, Alex Townsend
Learning elliptic partial differential equations with randomized linear algebra. CoRR (2021)
Yuji Nakatsukasa, Alex Townsend
Polynomial Approximants. SIAM J. Numer. Anal. 59 (1) (2021)
Daniel Fortunato, Nicholas Hale, Alex Townsend
The ultraspherical spectral element method. J. Comput. Phys. 436 (2021)
Heather Wilber, Anil Damle, Alex Townsend
Data-driven Algorithms for signal processing with rational functions. CoRR (2021)
Nicolas Boullé, Christopher J. Earls, Alex Townsend
Data-driven discovery of physical laws with human-understandable deep learning. CoRR (2021)
Nicolas Boullé, Alex Townsend
A generalization of the randomized singular value decomposition. CoRR (2021)
Tianyi Shi, Maximilian Ruth, Alex Townsend
Parallel algorithms for computing the tensor-train decomposition. CoRR (2021)
Matthew J. Colbrook, Andrew Horning, Alex Townsend
Computing Spectral Measures of Self-Adjoint Operators. SIAM Rev. 63 (3) (2021)
Tianyi Shi, Alex Townsend
On the Compressibility of Tensors. SIAM J. Matrix Anal. Appl. 42 (1) (2021)
Matthew J. Colbrook, Alex Townsend
Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems. CoRR (2021)
Nicolas Boullé, Yuji Nakatsukasa, Alex Townsend
Rational neural networks. NeurIPS (2020)
Austin R. Benson, Anil Damle, Alex Townsend
Over-parametrized neural networks as under-determined linear systems. CoRR (2020)
Nicolas Boullé, Alex Townsend
Computing with Functions in the Ball. SIAM J. Sci. Comput. 42 (4) (2020)
Matthew J. Colbrook, Andrew Horning, Alex Townsend
Computing spectral measures of self-adjoint operators. CoRR (2020)
Andrew Horning, Alex Townsend
FEAST for Differential Eigenvalue Problems. SIAM J. Numer. Anal. 58 (2) (2020)
Daniel Fortunato, Nicholas Hale, Alex Townsend
The ultraspherical spectral element method. CoRR (2020)
Nicolas Boullé, Yuji Nakatsukasa, Alex Townsend
Rational neural networks. CoRR (2020)
Yunan Yang, Alex Townsend, Daniel Appelö
Norm. CoRR (2020)
Sheehan Olver, Richard Mikaël Slevinsky, Alex Townsend
Fast algorithms using orthogonal polynomials. Acta Numer. 29 (2020)
Marc Aurèle Gilles, Alex Townsend
Continuous Analogues of Krylov Subspace Methods for Differential Operators. SIAM J. Numer. Anal. 57 (2) (2019)
Daniel Rubin, Alex Townsend
Bounding Zolotarev numbers using Faber rational functions. CoRR (2019)
Laurent Demanet, Alex Townsend
Stable Extrapolation of Analytic Functions. Found. Comput. Math. 19 (2) (2019)
Nicolas Boullé, Alex Townsend
Computing with functions in the ball. CoRR (2019)
Sheehan Olver, Alex Townsend, Geoffrey M. Vasil
A Sparse Spectral Method on Triangles. SIAM J. Sci. Comput. 41 (6) (2019)
Madeleine Udell, Alex Townsend
Why Are Big Data Matrices Approximately Low Rank? SIAM J. Math. Data Sci. 1 (1) (2019)
Bernhard Beckermann, Alex Townsend
Bounds on the Singular Values of Matrices with Displacement Structure. SIAM Rev. 61 (2) (2019)
Katherine N. Quinn, Heather Wilber, Alex Townsend, James P. Sethna
Chebyshev approximation and the global geometry of sloppy models. CoRR (2018)
Diego Ruiz-Antolín, Alex Townsend
A Nonuniform Fast Fourier Transform Based on Low Rank Approximation. SIAM J. Sci. Comput. 40 (1) (2018)
Alex Townsend, Marcus Webb, Sheehan Olver
Fast polynomial transforms based on Toeplitz and Hankel matrices. Math. Comput. 87 (312) (2018)
Yuji Nakatsukasa, Vanni Noferini, Alex Townsend
Vector Spaces of Linearizations for Matrix Polynomials: A Bivariate Polynomial Approach. SIAM J. Matrix Anal. Appl. 38 (1) (2017)
Heather Wilber, Alex Townsend, Grady B. Wright
Computing with Functions in Spherical and Polar Geometries II. The Disk. SIAM J. Sci. Comput. 39 (3) (2017)
Madeleine Udell, Alex Townsend
Nice latent variable models have log-rank. CoRR (2017)
Bernhard Beckermann, Alex Townsend
On the Singular Values of Matrices with Displacement Structure. SIAM J. Matrix Anal. Appl. 38 (4) (2017)
Laurent Demanet, Alex Townsend
Stable extrapolation of analytic functions. CoRR (2016)
Vanni Noferini, Alex Townsend
Numerical Instability of Resultant Methods for Multidimensional Rootfinding. SIAM J. Numer. Anal. 54 (2) (2016)
Alex Townsend, Heather Wilber, Grady B. Wright
Computing with Functions in Spherical and Polar Geometries I. The Sphere. SIAM J. Sci. Comput. 38 (4) (2016)
Yuji Nakatsukasa, Vanni Noferini, Alex Townsend
Computing the common zeros of two bivariate functions via Bézout resultants. Numerische Mathematik 129 (1) (2015)
Vanni Noferini, Alex Townsend
Are resultant methods numerically unstable for multidimensional rootfinding? CoRR (2015)
Alex Townsend, Sheehan Olver
The automatic solution of partial differential equations using a global spectral method. J. Comput. Phys. 299 (2015)
Alex Townsend
A Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions. SIAM J. Numer. Anal. 53 (4) (2015)
Nicholas Hale, Alex Townsend
A Fast, Simple, and Stable Chebyshev-Legendre Transform Using an Asymptotic Formula. SIAM J. Sci. Comput. 36 (1) (2014)
Nicholas Hale, Alex Townsend
An Algorithm for the Convolution of Legendre Series. SIAM J. Sci. Comput. 36 (3) (2014)
Sheehan Olver, Alex Townsend
A practical framework for infinite-dimensional linear algebra. HPTCDL@SC (2014)
Sheehan Olver, Alex Townsend
A Fast and Well-Conditioned Spectral Method. SIAM Rev. 55 (3) (2013)
Alex Townsend, Lloyd N. Trefethen
An Extension of Chebfun to Two Dimensions. SIAM J. Sci. Comput. 35 (6) (2013)
Nicholas Hale, Alex Townsend
Fast and Accurate Computation of Gauss-Legendre and Gauss-Jacobi Quadrature Nodes and Weights. SIAM J. Sci. Comput. 35 (2) (2013)