Here are three images from my research:
Y. Yang, A. Townsend, D. Appelö, Anderson acceleration using the H^{-s} norm, submitted.
N. Boulle and A. Townsend, Computing with functions on the ball, submitted, pdf
A. Townsend, M. Stillman, and Steven H. Strogatz, Circulant networks of identical Kuramoto oscillators: Seeking the densest network that does not globally synchronize and the sparsest one that does, submitted, pdf
S. Olver, A. Townsend, and G. Vasil, A sparse spectral method on triangles, to appear in SISC pdf
Y. Nakatsukasa and A. Townsend, Error localization of best L1 polynomial approximants, submitted, pdf
B. Beckermann and A. Townsend, Bounds on the singular values of matrices with displacement structure, SIAM Review, 61 (2019), pp. 319-344.
A. Horning and A. Townsend, FEAST for differential eigenvalue problems, to appear in SINUM pdf
T. Shi and A. Townsend, On the numerical ranks of tensors, submitted, pdf
K. N. Quinn, H. Wilber, A. Townsend, and J. P. Sethna, Chebyshev approximation and the global geometry of sloppy models, Physical Review Letters, 122, 158302 pdf.
M. A. Gilles and A. Townsend, Continuous analogues of Krylov methods for differential operators, SINUM, 57 (2019), pp. 899-924. pdf
S. Olver, A. Townsend, and G. M. Vasil, Recurrence relations for orthogonal polynomials on a triangle, to appear in ICOSAHOM Proceedings, pdf.
A. Townsend and H. Wilber, On the singular values of matrices with high displacement rank, Lin. Alg. Appl., 548 (2018), pp. 19-41. pdf
D. Fortunato and A. Townsend, Fast Poisson solvers for spectral methods, to appear in IMA Numer. Anal., pdf
J. Słomka, A. Townsend, and J. Dunkel, Stokes' second problem and an Einstein-de Haas analogue effect in active fluids, Physical Review Fluids, 3 (2018) pdf
M. Udell and A. Townsend, Why are big data matrices approximately low rank?, SIMODS, 1 (2019), pp. 144-160. pdf
D. Ruiz-Antolin and A. Townsend, A nonuniform fast Fourier transform based on low rank approximation, SISC, 40 (2018), A529-A547. pdf
B. Beckermann and A. Townsend, On the singular values of matrices with displacement structure, SIMAX, 38 (2017), pp. 1227-1248. pdf
L. Demanet and A. Townsend, Stable extrapolation of analytic functions, Found. Comput. Math., (2016), pp. 1-35. pdf
A. Townsend, M. Webb, and S. Olver, Fast polynomial transforms based on Toeplitz and Hankel matrices, Math. Comp., 87 (2018), pp. 1913-1934. pdf
H. Wilber, A. Townsend, and G. B. Wright, Computing with functions in spherical and polar geometrices II. The disk, SISC, 39 (2017), C238-C262. pdf
A. Townsend, Gaussian elimination corrects pivoting mistakes, submitted, pdf
A. Townsend, H. Wilber, and G. B. Wright, Computing with functions in spherical and polar geometries I. The sphere, SISC, 38 (2016), C403-C425. pdf
V. Noferini and A. Townsend, Numerical instability of resultant methods for multidimensional rootfinding, SINUM, 54 (2016), pp. 719-743. pdf
N. Hale and A. Townsend, A fast FFT-based discrete Legendre transform, IMA Numer. Anal., 36 (2016), pp. 1670-1684. pdf
A.Townsend, A fast analysis-based discrete Hankel transform using asymptotic expansions, SINUM, 53 (2015), pp. 1897-1917. pdf
A. Townsend, The race for high order Gauss-Legendre quadrature, in SIAM News, March 2015. pdf
A. Townsend, T. Trogdon, and S. Olver, Fast computation of Gauss quadrature nodes and weights on the whole real line, IMA Numer. Anal., 36 (2016), pp. 337-358. pdf.
S. Olver and A. Townsend, A practical framework for infinite-dimensional linear algebra, in HPTCDL 2014, IEEE press, pp. 57-62. pdf
A. Townsend and S. Olver, The automatic solution of partial differential equations using a global spectral method, J. Comput. Phys., 299, 2015, pp. 106-123. pdf
N. Hale and A. Townsend, An algorithm for the convolution of Legendre series, SISC, 36 (2014), A1207-A1220. pdf
A. Townsend and L. N. Trefethen, Continuous analogues of matrix factorizations, Proc. R. Soc. A., 471 (2015). pdf
N. Hale and A. Townsend, A fast, simple, and stable Chebyshev--Legendre transform using an asymptotic formula, SISC, 36 (2014), pp. A148-A167. pdf
S. Olver and A. Townsend, Fast inverse transform sampling in one and two dimensions, submitted. pdf
Y. Nakatsukasa, V. Noferini, and A. Townsend, Computing the common zeros of two bivariate functions via Bezout resultants, Numerische Mathematik, 129 (2015), pp 181-209. pdf
A. Townsend and L. N. Trefethen, An extension of Chebfun to two dimensions, SISC, 35 (2013), pp. C495-C518. pdf
Y. Nakatsukasa, V. Noferini, and A. Townsend, Vector spaces of linearizations for matrix polynomials: A bivariate polynomial approach, SIMAX, 38 (2017), pp. 1-29. pdf
A. Townsend and L. N. Trefethen, Gaussian elimination as an iterative algorithm, SIAM News, March 2013. pdf
N. Hale and A. Townsend, Fast and accurate computation of Gauss--Legendre and Gauss--Jacobi quadrature nodes and weights, SISC, 35 (2013), pp. A652-A672. pdf
S. Olver and A. Townsend, A fast and well-conditioned spectral method, SIAM Review, 55 (2013), pp. 462-489. pdf
A. Townsend and H. Wendland, Multiscale analysis in Sobolev spaces on bounded domains with zero boundary values, IMA J. Numer. Anal., 33 (2013), pp. 1095-1114. pdf