A Fast and Well-Conditioned Spectral Method. - Sheehan Olver; Alex Townsend (SIAM Rev., 2013)

Fast and Accurate Computation of Gauss-Legendre and Gauss-Jacobi Quadrature Nodes and Weights. - Nicholas Hale; Alex Townsend (SIAM J. Sci. Comput., 2013)

An Extension of Chebfun to Two Dimensions. - Alex Townsend; Lloyd N. Trefethen (SIAM J. Sci. Comput., 2013)

A practical framework for infinite-dimensional linear algebra. - Sheehan Olver; Alex Townsend (HPTCDL@SC, 2014)

A Fast, Simple, and Stable Chebyshev-Legendre Transform Using an Asymptotic Formula. - Nicholas Hale; Alex Townsend (SIAM J. Sci. Comput., 2014)

An Algorithm for the Convolution of Legendre Series. - Nicholas Hale; Alex Townsend (SIAM J. Sci. Comput., 2014)

Are resultant methods numerically unstable for multidimensional rootfinding? - Vanni Noferini; Alex Townsend (CoRR, 2015)

The automatic solution of partial differential equations using a global spectral method. - Alex Townsend; Sheehan Olver (J. Comput. Phys., 2015)

Computing the common zeros of two bivariate functions via Bézout resultants. - Yuji Nakatsukasa; Vanni Noferini; Alex Townsend (Numerische Mathematik, 2015)

A Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions. - Alex Townsend (SIAM J. Numer. Anal., 2015)

Numerical Instability of Resultant Methods for Multidimensional Rootfinding. - Vanni Noferini; Alex Townsend (SIAM J. Numer. Anal., 2016)

Computing with Functions in Spherical and Polar Geometries I. The Sphere. - Alex Townsend; Heather Wilber; Grady B. Wright (SIAM J. Sci. Comput., 2016)

Nice latent variable models have log-rank. - Madeleine Udell; Alex Townsend (CoRR, 2017)

On the Singular Values of Matrices with Displacement Structure. - Bernhard Beckermann; Alex Townsend (SIAM J. Matrix Anal. Appl., 2017)

Vector Spaces of Linearizations for Matrix Polynomials: A Bivariate Polynomial Approach. - Yuji Nakatsukasa; Vanni Noferini; Alex Townsend (SIAM J. Matrix Anal. Appl., 2017)

Computing with Functions in Spherical and Polar Geometries II. The Disk. - Heather Wilber; Alex Townsend; Grady B. Wright (SIAM J. Sci. Comput., 2017)

Chebyshev approximation and the global geometry of sloppy models. - Katherine N. Quinn; Heather Wilber; Alex Townsend; James P. Sethna (CoRR, 2018)

Fast polynomial transforms based on Toeplitz and Hankel matrices. - Alex Townsend; Marcus Webb; Sheehan Olver (Math. Comput., 2018)

A Nonuniform Fast Fourier Transform Based on Low Rank Approximation. - Diego Ruiz-Antolín; Alex Townsend (SIAM J. Sci. Comput., 2018)

Bounding Zolotarev numbers using Faber rational functions. - Daniel Rubin; Alex Townsend (CoRR, 2019)

Stable Extrapolation of Analytic Functions. - Laurent Demanet; Alex Townsend (Found. Comput. Math., 2019)

Continuous Analogues of Krylov Subspace Methods for Differential Operators. - Marc Aurèle Gilles; Alex Townsend (SIAM J. Numer. Anal., 2019)

Bounds on the Singular Values of Matrices with Displacement Structure. - Bernhard Beckermann; Alex Townsend (SIAM Rev., 2019)

A Sparse Spectral Method on Triangles. - Sheehan Olver; Alex Townsend; Geoffrey M. Vasil (SIAM J. Sci. Comput., 2019)

Why Are Big Data Matrices Approximately Low Rank? - Madeleine Udell; Alex Townsend (SIAM J. Math. Data Sci., 2019)

Rational neural networks. - Nicolas Boullé; Yuji Nakatsukasa; Alex Townsend (NeurIPS, 2020)

Fast algorithms using orthogonal polynomials. - Sheehan Olver; Richard Mikaël Slevinsky; Alex Townsend (Acta Numer., 2020)

Anderson Acceleration Using the H-s Norm. - Yunan Yang; Alex Townsend; Daniel Appelö (CoRR, 2020)

Over-parametrized neural networks as under-determined linear systems. - Austin R. Benson; Anil Damle; Alex Townsend (CoRR, 2020)

FEAST for Differential Eigenvalue Problems. - Andrew J. Horning; Alex Townsend (SIAM J. Numer. Anal., 2020)

Computing with Functions in the Ball. - Nicolas Boullé; Alex Townsend (SIAM J. Sci. Comput., 2020)

An optimal complexity spectral method for Navier-Stokes simulations in the ball. - Nicolas Boullé; Jonasz Slomka; Alex Townsend (CoRR, 2021)

Data-driven discovery of physical laws with human-understandable deep learning. - Nicolas Boullé; Christopher J. Earls; Alex Townsend (CoRR, 2021)

Data-driven Algorithms for signal processing with rational functions. - Heather Wilber; Anil Damle; Alex Townsend (CoRR, 2021)

Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks. - Annan Yu; Chloé Becquey; Diana Halikias; Matthew Esmaili Mallory; Alex Townsend (CoRR, 2021)

Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems. - Matthew J. Colbrook; Alex Townsend (CoRR, 2021)

The ultraspherical spectral element method. - Daniel Fortunato; Nicholas Hale; Alex Townsend (J. Comput. Phys., 2021)

On the Compressibility of Tensors. - Tianyi Shi; Alex Townsend (SIAM J. Matrix Anal. Appl., 2021)

Error Localization of Best L1 Polynomial Approximants. - Yuji Nakatsukasa; Alex Townsend (SIAM J. Numer. Anal., 2021)

Computing Spectral Measures of Self-Adjoint Operators. - Matthew J. Colbrook; Andrew J. Horning; Alex Townsend (SIAM Rev., 2021)

A generalization of the randomized singular value decomposition. - Nicolas Boullé; Alex Townsend (ICLR, 2022)

Probabilistic Missing Value Imputation for Mixed Categorical and Ordered Data. - Yuxuan Zhao; Alex Townsend; Madeleine Udell (NeurIPS, 2022)

On the stability of unevenly spaced samples for interpolation and quadrature. - Annan Yu; Alex Townsend (CoRR, 2022)

Learning Green's functions associated with parabolic partial differential equations. - Nicolas Boullé; Seick Kim; Tianyi Shi; Alex Townsend (CoRR, 2022)

A Quadrature Perspective on Frequency Bias in Neural Network Training with Nonuniform Data. - Annan Yu; Yunan Yang; Alex Townsend (CoRR, 2022)

Matrix recovery from matrix-vector products. - Diana Halikias; Alex Townsend (CoRR, 2022)

Anderson acceleration based on the H-s Sobolev norm for contractive and noncontractive fixed-point operators. - Yunan Yang; Alex Townsend; Daniel Appelö (J. Comput. Appl. Math., 2022)

Learning Green's functions associated with time-dependent partial differential equations. - Nicolas Boullé; Seick Kim; Tianyi Shi; Alex Townsend (J. Mach. Learn. Res., 2022)

Data-Driven Algorithms for Signal Processing with Trigonometric Rational Functions. - Heather Wilber; Anil Damle; Alex Townsend (SIAM J. Sci. Comput., 2022)

Tuning Frequency Bias in Neural Network Training with Nonuniform Data. - Annan Yu; Yunan Yang; Alex Townsend (ICLR, 2023)

Elliptic PDE learning is provably data-efficient. - Nicolas Boullé; Diana Halikias; Alex Townsend (CoRR, 2023)

Leveraging the Hankel norm approximation and block-AAA algorithms in reduced order modeling. - Annan Yu; Alex Townsend (CoRR, 2023)

Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems. - Matthew J. Colbrook; Qin Li; Ryan V. Raut; Alex Townsend (CoRR, 2023)

A Mathematical Guide to Operator Learning. - Nicolas Boullé; Alex Townsend (CoRR, 2023)

Operator learning for hyperbolic partial differential equations. - Christopher Wang; Alex Townsend (CoRR, 2023)

Learning Elliptic Partial Differential Equations with Randomized Linear Algebra. - Nicolas Boullé; Alex Townsend (Found. Comput. Math., 2023)

Parallel Algorithms for Computing the Tensor-Train Decomposition. - Tianyi Shi; Maximilian Ruth; Alex Townsend (SIAM J. Sci. Comput., 2023)

Operator learning without the adjoint. - Nicolas Boullé; Diana Halikias; Samuel E. Otto; Alex Townsend (CoRR, 2024)

How to reveal the rank of a matrix? - Anil Damle; Silke Glas; Alex Townsend; Annan Yu (CoRR, 2024)

Numerical Instability of Algebraic Rootfinding Methods. - Emil Graf; Alex Townsend (CoRR, 2024)

Are Sketch-and-Precondition Least Squares Solvers Numerically Stable? - Maike Meier; Yuji Nakatsukasa; Alex Townsend; Marcus Webb (SIAM J. Matrix Anal. Appl., 2024)

Structured matrix recovery from matrix-vector products. - Diana Halikias; Alex Townsend (Numer. Linear Algebra Appl., 2024)

Leveraging the Hankel norm approximation and data-driven algorithms in reduced order modeling. - Annan Yu; Alex Townsend (Numer. Linear Algebra Appl., 2024)

Extending Mercer's expansion to indefinite and asymmetric kernels. - Sungwoo Jeong; Alex Townsend (ICLR, 2025)

Avoiding Discretization Issues for Nonlinear Eigenvalue Problems. - Matthew J. Colbrook; Alex Townsend (SIAM J. Matrix Anal. Appl., 2025)

ContHutch++: Stochastic Trace Estimation For Implicit Integral Operators. - Jennifer Zvonek; Andrew J. Horning; Alex Townsend (SIAM J. Numer. Anal., 2025)

A Hidden Variable Resultant Method for the Polynomial Multiparameter Eigenvalue Problem. - Emil Graf; Alex Townsend (CoRR, 2025)